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Pertanyaan

fraction numerator open parentheses scriptbase log space 27 end scriptbase presuperscript 3 close parentheses squared minus open parentheses log presuperscript 3 space 9 close parentheses squared over denominator log presuperscript 3 space square root of 27 end fraction equals....

  1. 2 space

  2. 10 over 3 space

  3. 20 over 3 space

  4. 15 over 3 space

  5. 7 space

Pembahasan Soal:

Diketahui 27 equals 3 cubed comma space 9 equals 3 squared comma space d a n space square root of 27 equals square root of 3 cubed end root equals 3 to the power of 3 over 2 end exponent. Berdasarkan sifat logaritma scriptbase log open parentheses a close parentheses to the power of n equals n cross times log presuperscript a open parentheses a close parentheses end scriptbase presuperscript a dan scriptbase log open parentheses a close parentheses equals 1 end scriptbase presuperscript amaka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses scriptbase log space 27 end scriptbase presuperscript 3 close parentheses squared minus open parentheses log presuperscript 3 space 9 close parentheses squared over denominator log presuperscript 3 space square root of 27 end fraction end cell equals cell fraction numerator open parentheses scriptbase log space 3 cubed end scriptbase presuperscript 3 close parentheses squared minus open parentheses log presuperscript 3 space 3 squared close parentheses squared over denominator log presuperscript 3 space 3 to the power of begin display style 3 over 2 end style end exponent end fraction end cell row blank equals cell fraction numerator open parentheses 3 cross times scriptbase log space 3 end scriptbase presuperscript 3 close parentheses squared minus open parentheses 2 cross times log presuperscript 3 space 3 close parentheses squared over denominator begin display style 3 over 2 end style cross times log presuperscript 3 space 3 end fraction end cell row blank equals cell fraction numerator open parentheses 3 cross times 1 close parentheses squared minus open parentheses 2 cross times 1 close parentheses squared over denominator begin display style 3 over 2 end style cross times 1 end fraction end cell row blank equals cell fraction numerator open parentheses 3 close parentheses squared minus open parentheses 2 close parentheses squared over denominator begin display style 3 over 2 end style end fraction end cell row blank equals cell open parentheses 9 minus 4 close parentheses divided by 3 over 2 end cell row blank equals cell 5 cross times 2 over 3 end cell row blank equals cell fraction numerator 10 over denominator begin display style 3 end style end fraction end cell end table


Oleh karena itu, jawaban yang benar adlah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. Febrianti

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 06 Juni 2021

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Pertanyaan yang serupa

Hitunglah

Pembahasan Soal:

Logaritma adalah suatu operasi invers atau kebalikan dari perpangkatan.

Terdapat dua sifat logaritma yang digunakan dalam proses penyelesaian, yaitu:

begin mathsize 14px style log presuperscript a space a equals 1 log presuperscript a space b to the power of m equals m times log presuperscript a space b end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 3 1 over 9 square root of 3 end cell equals cell log presuperscript 3 square root of 1 over 9 squared cross times 3 end root end cell row blank equals cell log presuperscript 3 square root of 1 over 3 to the power of 4 cross times 3 end root end cell row blank equals cell log presuperscript 3 square root of 3 to the power of negative 4 end exponent cross times 3 end root end cell row blank equals cell log presuperscript 3 square root of 3 to the power of negative 3 end exponent end root end cell row blank equals cell log presuperscript 3 space open parentheses 3 to the power of negative 3 end exponent close parentheses to the power of begin inline style 1 half end style end exponent end cell row blank equals cell log presuperscript 3 space 3 to the power of negative begin inline style 3 over 2 end style end exponent end cell row blank equals cell negative 3 over 2 cross times log presuperscript 3 space 3 end cell row blank equals cell negative 3 over 2 end cell end table end style 

Jadi, nilai begin mathsize 14px style log presuperscript 3 1 over 9 square root of 3 equals negative 3 over 2 end style.

0

Roboguru

Dengan menggunakan sifat-sifat logaritma tentukan nilai dari: a) 5log15+5log50−5log6

Pembahasan Soal:

Ingat sifat bentuk logatitma berikut.

alogaalogbnalog(bc)alog(cb)====1nalogbalogb+alogcalogbalogc

sehingga dapat ditentukan nilai dari bentuk logaritma berikut. 

5log15+5log505log6======5log(615×50)5log1255log5335log5313  

Dengan demikian, diperoleh 5log15+5log505log6=3.

0

Roboguru

Nilai dari 4log6⋅6log8⋅8log16 adalah ...

Pembahasan Soal:

Ingat,

Sifat-sifat logaritma

alogbblogcclogd=alogdanlogbm=nmalogbaloga=1

Berdasarkan sifat-sifat tersebut, diperoleh perhitungan sebagai berikut

4log66log88log16=====4log1641log4212(4log4)2(1)2

Dengan demikian, nilai dari 4log66log88log16 adalah 2. 

0

Roboguru

Hasil dari  adalah ....

Pembahasan Soal:

Ingat kembali sifat-sifat logaritma:

begin mathsize 14px style log presuperscript straight a space straight b times log presuperscript straight b space straight c equals log presuperscript straight a space straight c log presuperscript straight a space straight b minus log presuperscript straight a space straight c equals log presuperscript straight a space open parentheses straight b over straight c close parentheses log presuperscript straight a space straight b to the power of straight m equals straight m times log presuperscript straight a space straight b end style 

Maka:

begin mathsize 14px style fraction numerator log presuperscript 6 space 27 times log presuperscript square root of 3 end presuperscript space 36 minus log presuperscript 4 space begin display style 1 over 64 end style over denominator log presuperscript 6 space 36 minus log presuperscript 6 space 6 square root of 6 end fraction equals fraction numerator log presuperscript 6 space 3 cubed times log presuperscript 3 to the power of begin display style 1 half end style end exponent end presuperscript space 6 squared minus log presuperscript 2 squared end presuperscript space begin display style 2 to the power of negative 6 end exponent end style over denominator log presuperscript 6 space 6 squared minus log presuperscript 6 space 6 times 6 to the power of begin display style 1 half end style end exponent end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 3 times log presuperscript 6 space 3 times begin display style fraction numerator 2 over denominator begin display style 1 half end style end fraction end style log presuperscript 3 space 6 minus open parentheses begin display style fraction numerator negative 6 over denominator 2 end fraction end style close parentheses times log presuperscript 2 space begin display style 2 end style over denominator log presuperscript 6 space 6 squared minus log presuperscript 6 space 6 to the power of begin display style 3 over 2 end style end exponent end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 3 times 4 times log presuperscript 6 space 3 times log presuperscript 3 space 6 plus 3 times 1 over denominator log presuperscript 6 space begin display style 6 squared over 6 to the power of begin display style 3 over 2 end style end exponent end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 12 times log presuperscript 6 space 6 plus 3 over denominator log presuperscript 6 space 6 to the power of begin display style 1 half end style end exponent end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 12 times 1 plus 3 over denominator begin display style 1 half end style times log presuperscript 6 space 6 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 12 plus 3 over denominator begin display style 1 half end style times 1 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 15 over denominator begin display style 1 half end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 30 end style  

Jadi, hasilnya adalah begin mathsize 14px style 30 end style.

0

Roboguru

hasil dari  adalah ....

Pembahasan Soal:

Dengan menggunakan sifat-sifat logaritma diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space 16 plus log presuperscript 3 space 9 end cell equals cell log presuperscript 2 space 2 to the power of 4 plus log presuperscript 3 space 3 squared end cell row blank equals cell 4 cross times scriptbase log space 2 end scriptbase presuperscript 2 plus space 2 cross times log presuperscript 3 space 3 end cell row blank equals cell 4 plus 2 end cell row blank equals 6 end table end style

Jadi, jawaban yang tepat adalah C.

0

Roboguru

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