Pertanyaan

Jika 5 lo g 3 = a dan 2 lo g 5 = b maka 40 lo g 15 = ...

Jika $^{5} lo g 3 = a$ dan $^{2} lo g 5 = b$ maka $^{40} lo g 15 = ...$

$fraction numerator a b plus b over denominator b plus 3 end fraction$
$fraction numerator a b plus a over denominator a plus 3 end fraction$
$fraction numerator a b plus 3 over denominator a plus b end fraction$
$fraction numerator a plus 3 over denominator a b plus b end fraction$
$fraction numerator b plus 3 over denominator a b plus b end fraction$

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Ingat kembali sifat logaritma berikut! Oleh karena itu, diperoleh perhitungan sebagai berikut. Jadi, diperoleh . Oleh karena itu, jawaban yang benar adalah A.

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.