Pertanyaan

Diketahui 2 lo g 3 = x dan 2 lo g 10 = y . Nilai 6 lo g 120 = ...

Diketahui $^{2} lo g 3 = x$ dan $^{2} lo g 10 = y$ . Nilai $^{6} lo g 120 = ...$

$fraction numerator x plus y plus 2 over denominator x plus 1 end fraction$
$fraction numerator x plus 1 over denominator x plus y plus 2 end fraction$
$fraction numerator x over denominator x y plus 2 end fraction$
$fraction numerator x y plus 2 over denominator x end fraction$
$fraction numerator 2 x y over denominator x plus 1 end fraction$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat sifat logaritma Sehingga Dengan demikian, jawaban yang tepat adalah A.

Ingat sifat logaritma

$table attributes columnalign right center left columnspacing 0px end attributes row cell blank to the power of a log space open parentheses b c close parentheses equals to the power of a log space b plus to the power of b log space c to the power of a log space b end cell equals cell fraction numerator blank to the power of p log space b over denominator blank to the power of p log space a end fraction end cell end table$

Sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell space to the power of 6 log space 120 end cell equals cell fraction numerator blank squared log space 120 over denominator blank squared log space 6 end fraction end cell row blank equals cell fraction numerator blank squared log space open parentheses 4 cross times 3 cross times 10 close parentheses over denominator blank squared log space open parentheses 2 cross times 3 close parentheses end fraction end cell row blank equals cell fraction numerator blank squared log space 4 plus squared log space 3 plus squared log space 10 over denominator blank squared log space 2 plus squared log space 3 end fraction end cell row blank equals cell fraction numerator 2 plus x plus y over denominator 1 plus x end fraction end cell row blank equals cell fraction numerator x plus y plus 2 over denominator x plus 1 end fraction end cell end table$

Dengan demikian, jawaban yang tepat adalah A.