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Jika , maka  = ....

Pertanyaan

Jika begin mathsize 14px style log presubscript space presuperscript 8 space 5 equals p end style, maka begin mathsize 14px style log presubscript space presuperscript 16 space 10 end style = ....

  1. 3p

  2. begin mathsize 14px style p cubed end style

  3. 4(3p + 1)

  4. begin mathsize 14px style fraction numerator 3 p plus 1 over denominator 4 end fraction end style

  5. begin mathsize 14px style fraction numerator p plus 3 over denominator 4 end fraction end style

Pembahasan Soal:

begin mathsize 14px style log presubscript space presuperscript 8 space 5 equals log presubscript space presuperscript 2 cubed end presuperscript space 5 equals 1 third space log presubscript space presuperscript 2 space 5  1 third space log presubscript space presuperscript 2 space 5 equals p rightwards double arrow log presubscript space presuperscript 2 space 5 equals 3 p    log presubscript space presuperscript 16 space 10 equals log presubscript space presuperscript 16 space 5 space. space 2  space space space space space space space space space space space space space equals log presubscript space presuperscript 16 space 5 plus log presubscript space presuperscript 16 space 2  space space space space space space space space space space space space space equals log presubscript space presuperscript 2 to the power of 4 end presuperscript space 5 plus log presubscript space presuperscript 2 to the power of 4 end presuperscript space 2  space space space space space space space space space space space space space equals 1 fourth log presubscript space presuperscript 2 space 5 plus 1 fourth log presubscript space presuperscript 2 space 2  space space space space space space space space space space space space space equals 1 fourth open parentheses 3 p close parentheses plus 1 fourth open parentheses 1 close parentheses  space space space space space space space space space space space space space equals fraction numerator 3 p plus 1 over denominator 4 end fraction end style

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Rizky

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 04 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui fungsi f(x)=41​log(2x2+x+8). Nilai f(8)=...

Pembahasan Soal:

Diketahui fungsi f open parentheses x close parentheses equals to the power of 1 fourth end exponent log space open parentheses 2 x squared plus x plus 8 close parentheses. Substitusi nilai x equals 8, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f open parentheses 8 close parentheses equals to the power of 1 fourth end exponent log space open parentheses 2 open parentheses 8 close parentheses squared plus open parentheses 8 close parentheses plus 8 close parentheses end cell row blank blank cell equals to the power of 1 fourth end exponent log space open parentheses 128 plus 8 plus 8 close parentheses end cell row blank blank cell equals to the power of 1 fourth end exponent log space open parentheses 128 plus 8 plus 8 close parentheses end cell row blank blank cell equals to the power of 1 fourth end exponent log space 144 end cell row blank blank cell equals to the power of 1 fourth end exponent log space open parentheses 16 cross times 9 close parentheses end cell row blank blank cell equals to the power of 1 fourth end exponent log space 16 plus to the power of 1 fourth end exponent log space 9 end cell row blank equals cell space to the power of 4 to the power of negative 1 end exponent end exponent log space 4 squared plus to the power of 2 to the power of negative 2 end exponent end exponent log space 3 squared end cell row blank equals cell fraction numerator 2 over denominator negative 1 end fraction cross times to the power of 4 log space 4 plus fraction numerator 2 over denominator negative 2 end fraction cross times squared log space 3 end cell row blank equals cell negative 2 cross times 1 plus open parentheses negative 1 close parentheses cross times squared log space 3 end cell row blank equals cell negative 2 minus squared log space 3 end cell row blank equals cell negative squared log space 3 minus 2 end cell end table  

Jadi, nilai f open parentheses 8 close parentheses equals minus squared log space 3 minus 2

Dengan demikian, jawaban yang tepat adalah A.

2

Roboguru

Grafik dari y=2logx1​ adalah ...

Pembahasan Soal:

Diketahui: Fungsi y equals scriptbase log invisible function application 1 over x end scriptbase presuperscript 2

Ditanya: Grafik dari y equals scriptbase log invisible function application 1 over x end scriptbase presuperscript 2 adalah ...

Jawab:

Untuk menentukan grafik dari suatu logaritma sama hal nya dengan menentukan grafik dari suatu fungsi yaitu dengan ambil beberapa titik absis secara acak, untuk mempermudah perhitungan maka pilih nilai yang menghasilkan nilai logaritma yang bagus dengan cara menyesuaikan dengan nilai basis dari logaritma tersebut.

Sebelum menentukan titik yang akan diambil maka akan dilakukan menyederhanaan terlebih dahulu ke fungsi logaritma yang diketahui dengan menggunakan sifat pada logaritma sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell scriptbase log invisible function application 1 over x end scriptbase presuperscript 2 end cell row blank equals cell scriptbase log invisible function application x to the power of negative 1 end exponent end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application x end scriptbase presuperscript 2 end cell end table

Didapatkan fungsi yang sudah disederhanakan yaitu y equals negative 1 times scriptbase log invisible function application x end scriptbase presuperscript 2.

Selanjutnya akan diambil titik absis dengan menyesuaikan nilai basis logaritmanya yaitu x equals 1 fourth comma blank 1 half comma blank 1 comma blank 4 comma blank 8.

Akan ditentukan titik koordinat

Untuk x equals 1 fourth

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell negative 1 times scriptbase log invisible function application x end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application 1 fourth end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application 1 over 2 squared end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application 2 to the power of negative 2 end exponent end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times negative 2 times scriptbase log invisible function application 2 end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times negative 2 times 1 end cell row blank equals 2 end table

Didapatkan titik open parentheses 1 fourth comma 2 close parentheses

Untuk x equals 1 half

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell negative 1 times scriptbase log invisible function application x end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application 1 half end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application 1 over 2 to the power of negative 1 end exponent end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application 2 to the power of negative 1 end exponent end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times negative 1 times scriptbase log invisible function application 2 end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times negative 1 times 1 end cell row blank equals 1 end table

Didapatkan titik open parentheses 1 half comma 1 close parentheses

Untuk x equals 1

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell negative 1 times scriptbase log invisible function application x end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application 1 end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times 0 end cell row blank equals 0 end table

Didapatkan titik open parentheses 1 , 0 close parentheses

Untuk x equals 4

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell negative 1 times scriptbase log invisible function application x end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application 4 end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application 2 squared end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times 2 times scriptbase log invisible function application 2 end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times 2 times 1 end cell row blank equals cell negative 2 end cell end table

Didapatkan titik open parentheses 4 comma negative 2 close parentheses

Untuk x equals 8

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell negative 1 times scriptbase log invisible function application x end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application 8 end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times scriptbase log invisible function application 2 cubed end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times 3 times scriptbase log invisible function application 2 end scriptbase presuperscript 2 end cell row blank equals cell negative 1 times 3 times 1 end cell row blank equals cell negative 3 end cell end table

Didapatkan titik open parentheses 8 comma negative 3 close parentheses

Berdasarkan hasil titik-titik koordinat yang sudah didapatkan maka dapat dibuat sebuah grafik fungsi dari logaritma y equals scriptbase log invisible function application 1 over x end scriptbase presuperscript 2 seperti gambar berikut.

Jadi, dapat disimpulkan bahwa grafik dari y equals scriptbase log invisible function application 1 over x end scriptbase presuperscript 2 adalah seperti gambar di atas.

Oleh karena itu, jawaban yang benar adalah E.

0

Roboguru

Nilai fungsi f(x)=4log(2x−6) untuk x=4 adalah ...

Pembahasan Soal:

Diketahui f open parentheses x close parentheses equals space to the power of 4 log space open parentheses 2 x minus 6 close parentheses. Substitusi nilai x equals 4 diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f open parentheses 4 close parentheses equals to the power of 4 log space open parentheses 2 open parentheses 4 close parentheses minus 6 close parentheses end cell row blank blank cell equals to the power of 4 log space open parentheses 8 minus 6 close parentheses end cell row blank blank cell equals to the power of 4 log space open parentheses 2 close parentheses end cell row blank equals cell space to the power of 2 squared end exponent log space 2 end cell row blank equals cell 1 half cross times squared log space 2 end cell row blank equals cell 1 half cross times 1 end cell row blank equals cell 1 half end cell end table 

Jadi, nilai fungsi f open parentheses x close parentheses equals space to the power of 4 log space open parentheses 2 x minus 6 close parentheses untuk x equals 4 adalah 1 half

Dengan demikian, jawaban yang tepat adalah C.

0

Roboguru

Hasil dari 3log315​(3log45)2−(3log5)2​ adalah...

Pembahasan Soal:

Ingat kembali pemfaktoran bentuk selisih kuadrat dan sifat logaritma berikut!

table attributes columnalign right center left columnspacing 0px end attributes row cell a squared minus b squared end cell equals cell left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis end cell row cell log presuperscript a space left parenthesis b c right parenthesis end cell equals cell log presuperscript a space b plus log presuperscript a space c end cell row cell log presuperscript a space b to the power of m end cell equals cell m space log presuperscript a space b end cell row cell log presuperscript a space a end cell equals 1 end table 

 

Dengan sifat-sifat di atas, diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator left parenthesis log presuperscript 3 space 45 right parenthesis squared minus left parenthesis log presuperscript 3 space 5 right parenthesis squared over denominator log presuperscript 3 space cube root of 15 end fraction end cell row blank equals cell fraction numerator left parenthesis log presuperscript 3 space 45 plus log presuperscript 3 space 5 right parenthesis left parenthesis log presuperscript 3 space 45 minus log presuperscript 3 space 5 right parenthesis over denominator log presuperscript 3 space 15 to the power of begin display style 1 third end style end exponent end fraction end cell row blank equals cell fraction numerator left parenthesis log presuperscript 3 space left parenthesis 9 times 5 right parenthesis plus log presuperscript 3 space 5 right parenthesis left parenthesis log presuperscript 3 space left parenthesis 9 times 5 right parenthesis minus log presuperscript 3 space 5 right parenthesis over denominator begin display style 1 third end style log presuperscript 3 space 15 end fraction end cell row blank equals cell fraction numerator left parenthesis log presuperscript 3 space 9 plus log presuperscript 3 space 5 plus log presuperscript 3 space 5 right parenthesis left parenthesis left parenthesis log presuperscript 3 space 9 plus log presuperscript 3 space 5 minus log presuperscript 3 space 5 right parenthesis over denominator 1 third log presuperscript 3 space left parenthesis 3 times 5 right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis log presuperscript 3 space 3 squared plus 2 times log presuperscript 3 space 5 right parenthesis left parenthesis log presuperscript 3 space 3 squared right parenthesis over denominator 1 third left parenthesis log presuperscript 3 space 3 plus log presuperscript 3 space 5 right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis 2 times log presuperscript 3 space 3 plus 2 times log presuperscript 3 space 5 right parenthesis left parenthesis 2 times log presuperscript 3 space 3 right parenthesis over denominator begin display style 1 third end style left parenthesis 1 plus log presuperscript 3 space 5 right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis 2 times 1 plus 2 times log presuperscript 3 space 5 right parenthesis left parenthesis 2 times 1 right parenthesis over denominator begin display style 1 third end style left parenthesis 1 plus log presuperscript 3 space 5 right parenthesis end fraction end cell row blank equals cell fraction numerator 2 times 2 up diagonal strike left parenthesis 1 plus log presuperscript 3 space 5 right parenthesis end strike over denominator begin display style 1 third end style up diagonal strike left parenthesis 1 plus log presuperscript 3 space 5 right parenthesis end strike end fraction end cell row blank equals cell fraction numerator 4 over denominator begin display style 1 third end style end fraction end cell row blank equals cell 4 times 3 over 1 end cell row blank equals 12 end table  

Dengan demikian, fraction numerator left parenthesis log presuperscript 3 space 45 right parenthesis squared minus left parenthesis log presuperscript 3 space 5 right parenthesis squared over denominator log presuperscript 3 space cube root of 15 end fraction equals 12.

Jadi, jawaban yang benar adalah C. 

0

Roboguru

Jika 5log3=a dan 2log5=b maka 40log15=...

Pembahasan Soal:

Ingat kembali sifat logaritma berikut!

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a space b end cell equals cell fraction numerator log presuperscript p space b over denominator log presuperscript p space a end fraction end cell row cell log presuperscript a space left parenthesis b c right parenthesis end cell equals cell log presuperscript a space b plus log presuperscript a space c end cell row cell log presuperscript a space b to the power of m end cell equals cell m space log presuperscript a space b end cell row cell fraction numerator 1 over denominator log presuperscript a space b end fraction end cell equals cell log presuperscript b space a end cell row cell log presuperscript a space a end cell equals cell 1 space end cell end table  

 

Oleh karena itu, diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 40 space 15 end cell equals cell fraction numerator log presuperscript 5 space 15 over denominator log presuperscript 5 space 40 end fraction end cell row blank equals cell fraction numerator log presuperscript 5 space left parenthesis 3 cross times 5 right parenthesis over denominator log presuperscript 5 space left parenthesis 2 cubed cross times 5 right parenthesis end fraction end cell row blank equals cell fraction numerator log presuperscript 5 space 3 plus log presuperscript 5 space 5 over denominator log presuperscript 5 space 2 cubed plus log presuperscript 5 space 5 end fraction end cell row blank equals cell fraction numerator a plus 1 over denominator 3 space log presuperscript 5 space 2 plus 1 end fraction end cell row blank equals cell fraction numerator a plus 1 over denominator 3 times begin display style 1 over b end style plus 1 end fraction end cell row blank equals cell fraction numerator a plus 1 over denominator begin display style 3 over b end style plus begin display style b over b end style end fraction end cell row blank equals cell fraction numerator a plus 1 over denominator left parenthesis begin display style fraction numerator 3 plus b over denominator b end fraction end style right parenthesis end fraction end cell row blank equals cell a plus 1 times fraction numerator b over denominator 3 plus b end fraction end cell row blank equals cell fraction numerator left parenthesis a plus 1 right parenthesis b over denominator 3 plus b end fraction end cell row blank equals cell fraction numerator a b plus b over denominator b plus 3 end fraction end cell end table 

Jadi, diperoleh log presuperscript 40 space 15 equals fraction numerator a b plus b over denominator b plus 3 end fraction.

Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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