Pertanyaan

Diketahui 2 lo g 3 = p dan 5 lo g 2 = q . Jika 45 lo g 36 dinyatakan dalam p dan q , maka adalah ....

Diketahui $_{2} lo g 3 = p dan_{5} lo g 2 = q$ . Jika $_{45} lo g 36$ dinyatakan dalam $p$ dan $q,$ maka adalah ....

$begin mathsize 14px style fraction numerator 2 p q plus 2 over denominator 2 p q plus q end fraction end style$
$fraction numerator size 14px 2 size 14px p size 14px q size 14px plus size 14px 2 size 14px q over denominator size 14px 2 size 14px p size 14px q size 14px plus size 14px 1 end fraction$
$fraction numerator size 14px p size 14px q size 14px plus size 14px 2 size 14px q over denominator size 14px p size 14px q size 14px plus size 14px 1 end fraction$
$fraction numerator size 14px p size 14px q size 14px plus size 14px 1 over denominator size 14px p size 14px q end fraction$

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Jawaban terverifikasi

Jawaban

jawaban yang tepatadalah B.

jawaban yang tepat adalah B.

Pembahasan

Ingat bahwa dengan dan adalah bilangan positif serta dan sehingga Jadi, jawaban yang tepatadalah B.

Ingat bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript presuperscript a invisible function application b end cell equals cell fraction numerator log presubscript presuperscript k invisible function application b over denominator log presubscript presuperscript k invisible function application b end fraction end cell row cell log presubscript presuperscript a invisible function application b end cell equals cell fraction numerator 1 over denominator log presubscript presuperscript b invisible function application a end fraction end cell row cell log presubscript presuperscript a invisible function application b plus log presubscript presuperscript a invisible function application c end cell equals cell log presubscript presuperscript a invisible function application b times c end cell row cell log presubscript presuperscript a invisible function application b to the power of m end cell equals cell m times log presubscript presuperscript a invisible function application b end cell row cell log presubscript presuperscript a invisible function application b times log presubscript presuperscript b invisible function application c end cell equals cell log presubscript presuperscript a invisible function application c end cell end table end style$

dengan dan adalah bilangan positif serta dan sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript presuperscript 45 invisible function application 36 end cell equals cell fraction numerator log presubscript presuperscript 3 invisible function application 36 over denominator log presubscript presuperscript 3 invisible function application 45 end fraction end cell row blank equals cell fraction numerator log presubscript presuperscript 3 invisible function application 9 times 4 over denominator log presubscript presuperscript 3 invisible function application 9 times 5 end fraction end cell row blank equals cell fraction numerator log presubscript presuperscript 3 invisible function application 9 plus log presubscript presuperscript 3 invisible function application 4 over denominator log presubscript presuperscript 3 invisible function application 9 plus log presubscript presuperscript 3 invisible function application 5 end fraction end cell row blank equals cell fraction numerator 2 plus log presubscript presuperscript 3 invisible function application 2 squared over denominator 2 plus log presubscript presuperscript 3 invisible function application 2 times log presubscript presuperscript 2 invisible function application 5 end fraction end cell row blank equals cell fraction numerator 2 plus 2 times log presubscript presuperscript 3 invisible function application 2 over denominator 2 plus fraction numerator 1 over denominator log presubscript presuperscript 2 invisible function application 3 end fraction times fraction numerator 1 over denominator log presubscript presuperscript 5 invisible function application 2 end fraction end fraction end cell row blank equals cell fraction numerator 2 plus 2 times fraction numerator 1 over denominator log presubscript presuperscript 2 invisible function application 3 end fraction over denominator 2 plus 1 over p times 1 over q end fraction end cell row blank equals cell fraction numerator 2 plus 2 over p over denominator 2 plus fraction numerator 1 over denominator p q end fraction end fraction end cell row blank equals cell fraction numerator fraction numerator 2 p plus 2 over denominator p end fraction over denominator fraction numerator 2 p q plus 1 over denominator p q end fraction end fraction end cell row blank equals cell fraction numerator 2 p q plus 2 q over denominator 2 p q plus 1 end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah B.