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Pertanyaan

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. 2 

  2. 1 

  3. 1 half 

  4. negative 1 

  5. negative 2 

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.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

L. Rante

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 11 Juli 2021

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Pertanyaan yang serupa

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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.

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Hasil dari .

Pembahasan Soal:

Gunakan sifat logaritma berikut:

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

Perhatikan perhitungan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator log presuperscript 3 space 36 times log presuperscript 6 space 81 plus log presuperscript 4 space 32 over denominator log presuperscript begin display style 1 over 9 end style end presuperscript space 27 end fraction end cell equals cell fraction numerator log presuperscript 3 space 6 squared times log presuperscript 6 space 81 plus log presuperscript 2 squared end presuperscript space 2 to the power of 5 over denominator log presuperscript begin display style 3 to the power of negative 2 end exponent end style end presuperscript space 3 cubed end fraction end cell row blank equals cell fraction numerator 2 log presuperscript 3 space 6 times log presuperscript 6 space 81 plus begin display style 5 over 2 end style space open parentheses 1 close parentheses over denominator begin display style fraction numerator 3 over denominator negative 2 end fraction end style space open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator 2 space log presuperscript 3 space 81 plus begin display style 5 over 2 end style over denominator begin display style negative 3 over 2 end style end fraction end cell row blank equals cell fraction numerator 2 space log presuperscript 3 space 3 to the power of 4 plus 5 over 2 over denominator begin display style negative 3 over 2 end style end fraction end cell row blank equals cell fraction numerator 2 cross times 4 space log presuperscript 3 space 3 plus begin display style 5 over 2 end style over denominator negative begin display style 3 over 2 end style end fraction end cell row blank equals cell fraction numerator 8 plus begin display style 5 over 2 end style over denominator negative begin display style 3 over 2 end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 16 plus 5 over denominator 2 end fraction end style over denominator negative begin display style 3 over 2 end style end fraction end cell row blank equals cell 21 over 2 cross times open parentheses negative 2 over 3 close parentheses end cell row cell fraction numerator log presuperscript 3 space 36 times log presuperscript 6 space 81 plus log presuperscript 4 space 32 over denominator log presuperscript begin display style 1 over 9 end style end presuperscript space 27 end fraction end cell equals cell negative 7 end cell end table end style

Jadi, diperoleh begin mathsize 14px style fraction numerator log presuperscript 3 space 36 times log presuperscript 6 space 81 plus log presuperscript 4 space 32 over denominator log presuperscript begin display style 1 over 9 end style end presuperscript space 27 end fraction equals negative 7 end style.

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Nilai dari  adalah ...

Pembahasan Soal:

Diketahui:

Persamaan logaritma begin mathsize 14px style scriptbase log space 27 equals scriptbase log space 3 end scriptbase presuperscript 5 end scriptbase presuperscript 3 x plus 2 end presuperscript end style.

Ingatlah sifat logaritma, yaitu: begin mathsize 14px style scriptbase log space straight b to the power of straight m equals straight m over straight n times space straight l presuperscript straight a og space straight b space end scriptbase presuperscript straight a to the power of straight n end presuperscript end style.

Sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell blank to the power of 3 x plus 2 end exponent log space 27 end cell equals cell scriptbase log space 3 end scriptbase presuperscript 5 to the power of 3 x plus 2 end exponent log space 27 equals scriptbase log space 3 cubed end scriptbase presuperscript 5 cubed end presuperscript to the power of 3 x plus 2 end exponent log space 27 equals scriptbase log space 27 end scriptbase presuperscript 125 end cell row cell 3 x plus 2 end cell equals 125 row cell 3 x end cell equals cell 125 minus 2 end cell row cell 3 x end cell equals 123 row x equals cell 123 over 3 end cell row x equals 41 end table end style

Nilai dari begin mathsize 14px style scriptbase log space 27 equals scriptbase log space 3 end scriptbase presuperscript 5 end scriptbase presuperscript 3 x plus 2 end presuperscript end style adalah begin mathsize 14px style 41 end style.

Jadi, jawaban yang tepat adalah B.

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Jika  dan  memenuhi persamaan . Maka  ...

Pembahasan Soal:

Diketahui:

Persamaan logaritma begin mathsize 14px style 2 open parentheses scriptbase log space x end scriptbase presuperscript 4 close parentheses squared minus 6 open parentheses scriptbase log space x over 2 end scriptbase presuperscript 4 close parentheses plus 1 equals 0 end style.

Jika begin mathsize 14px style scriptbase log space x equals a end scriptbase presuperscript 4 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 left parenthesis scriptbase log space x end scriptbase presuperscript 4 right parenthesis squared minus 6 open parentheses scriptbase log space x over 2 end scriptbase presuperscript 4 close parentheses plus 1 end cell equals 0 row cell 2 left parenthesis scriptbase log space x end scriptbase presuperscript 4 right parenthesis squared minus 6 open parentheses scriptbase log space x minus scriptbase log space 2 end scriptbase presuperscript 4 end scriptbase presuperscript 4 close parentheses plus 1 end cell equals 0 row cell 2 left parenthesis scriptbase log space x end scriptbase presuperscript 4 right parenthesis squared minus 6 open parentheses scriptbase log space x minus scriptbase log space 2 end scriptbase presuperscript 2 squared end presuperscript end scriptbase presuperscript 4 close parentheses plus 1 end cell equals 0 row cell 2 left parenthesis scriptbase log space x end scriptbase presuperscript 4 right parenthesis squared minus 6 open parentheses scriptbase log space x minus 1 half end scriptbase presuperscript 4 close parentheses plus 1 end cell equals 0 row cell 2 a squared minus 6 open parentheses a minus 1 half close parentheses plus 1 end cell equals 0 row cell 2 a squared minus 6 a plus 3 plus 1 end cell equals 0 row cell 2 a squared minus 6 a plus 4 end cell equals 0 row cell 2 open parentheses a squared minus 3 a plus 2 close parentheses end cell equals 0 row cell 2 open parentheses a open parentheses a minus 1 close parentheses minus 2 open parentheses a minus 1 close parentheses close parentheses end cell equals 0 row cell 2 open parentheses a minus 1 close parentheses open parentheses a minus 2 close parentheses end cell equals 0 end table end style

Dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a minus 1 end cell equals 0 row a equals 1 row blank blank blank row cell a minus 2 end cell equals 0 row a equals 2 end table end style

Dimisalkan begin mathsize 14px style scriptbase log space x equals a end scriptbase presuperscript 4 end style, maka persamaan logaritma menjadi:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log space x subscript 1 end scriptbase presuperscript 4 end cell equals a row cell scriptbase log space x subscript 1 end scriptbase presuperscript 4 end cell equals 1 row cell x subscript 1 end cell equals cell 4 to the power of 1 end cell row cell x subscript 1 end cell equals 4 row blank blank blank row cell scriptbase log space x subscript 2 end scriptbase presuperscript 4 end cell equals a row cell scriptbase log space x subscript 2 end scriptbase presuperscript 4 end cell equals 2 row cell x subscript 2 end cell equals cell 4 squared end cell row cell x subscript 2 end cell equals 16 end table end style

Maka begin mathsize 14px style x subscript 1 plus x subscript 2 equals end stylebegin mathsize 14px style 4 plus 16 equals 20 end style.

Jadi, jawaban yang tepat adalah E.

Roboguru

.

Pembahasan Soal:

Gunakan sifat bentuk logaritma berikut:

table attributes columnalign right center left columnspacing 2px end attributes row cell log presuperscript a space a end cell equals 1 row cell log presuperscript a to the power of n end presuperscript space open parentheses b to the power of m close parentheses end cell equals cell m over n space open parentheses log presuperscript a space b close parentheses end cell end table

Karena 27 equals 3 cubed, maka menggunakan sifat bentuk logaritma di atas dapat dihitung nilai log presuperscript 27 space 3 sebagai berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell log presuperscript 27 space 3 end cell equals cell log presuperscript 3 cubed end presuperscript space 3 to the power of 1 end cell row blank equals cell 1 third open parentheses log presuperscript 3 space 3 close parentheses end cell row blank equals cell 1 third times 1 end cell row cell log presuperscript 27 space 3 end cell equals cell 1 third end cell end table

Diperoleh bahwa table attributes columnalign right center left columnspacing 2px end attributes row cell log presuperscript 27 space 3 end cell equals cell 1 third end cell end table.

Jadi, jawaban yang tepat adalah E.

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