Pertanyaan

Diketahui 2 lo g 3 = p dan 3 lo g 5 = q .Jika 75 lo g 60 dinyatakan dalam p dan q , maka adalah ....

Diketahui $_{2} lo g 3 = p dan_{3} lo g 5 = q$ . Jika $_{75} lo g 60$ dinyatakan dalam $p$ dan $q,$ maka adalah ....

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

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingat bahwa dengan dan adalah bilangan positif serta dan sehingga Jadi, jawaban yang tepat adalah D.

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 blank presuperscript 75 invisible function application 60 end cell equals cell fraction numerator log presubscript blank presuperscript 2 invisible function application 60 over denominator log presubscript blank presuperscript 2 invisible function application 75 end fraction end cell row blank equals cell fraction numerator log presubscript blank presuperscript 2 invisible function application 4 times 3 times 5 over denominator log presubscript blank presuperscript 2 invisible function application 3 times 25 end fraction end cell row blank equals cell fraction numerator left parenthesis log presubscript blank presuperscript 2 invisible function application 4 right parenthesis plus left parenthesis log presubscript blank presuperscript 2 invisible function application 3 right parenthesis plus left parenthesis log presubscript blank presuperscript 2 invisible function application 5 right parenthesis over denominator left parenthesis log presubscript blank presuperscript 2 invisible function application 3 right parenthesis plus left parenthesis log presubscript blank presuperscript 2 invisible function application 25 right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis 2 right parenthesis plus left parenthesis p right parenthesis plus left parenthesis log presubscript blank presuperscript 2 invisible function application 3 times log presubscript blank presuperscript 3 invisible function application 5 right parenthesis over denominator left parenthesis p right parenthesis plus left parenthesis log presubscript blank presuperscript 2 invisible function application 5 squared right parenthesis end fraction end cell row blank equals cell fraction numerator 2 plus p plus p q over denominator p plus 2 log presubscript blank presuperscript 2 invisible function application 5 end fraction end cell row blank equals cell fraction numerator 2 plus p plus p q over denominator p plus 2 times log presubscript blank presuperscript 2 invisible function application 3 times log presubscript blank presuperscript 3 invisible function application 5 end fraction end cell row blank equals cell fraction numerator 2 plus p plus p q over denominator p plus 2 p q end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah D.