Pertanyaan

Jika 2 lo g 10 = p + 1 2 p dan 3 lo g 5 = 3 q , maka 2 − 12 lo g 15 = ....

Jika $_{2} lo g 10 = \frac{2 p}{p + 1}$ dan $_{3} lo g 5 = \frac{q}{3}$ , maka $2 -_{12} lo g 15 =$ ....

$begin mathsize 14px style fraction numerator negative 2 p q plus p plus 3 q minus 6 over denominator negative 7 p q plus 3 q plus 5 p minus 3 end fraction end style$
$begin mathsize 14px style fraction numerator 2 p q plus 2 p plus 3 q minus 3 over denominator negative 7 p q plus 3 q plus 5 p minus 3 end fraction end style$
$begin mathsize 14px style fraction numerator 3 p q minus 2 p minus 4 q plus 2 over denominator 2 p q plus 2 p plus 3 q minus 3 end fraction end style$
$begin mathsize 14px style fraction numerator 2 p q plus p minus 2 q minus 4 over denominator 2 p q plus 2 q plus 3 p minus 3 end fraction end style$
$fraction numerator size 14px 3 size 14px p size 14px q size 14px plus size 14px 3 size 14px p size 14px plus size 14px 5 size 14px q size 14px minus size 14px 3 over denominator size 14px 2 size 14px p size 14px q size 14px plus size 14px 2 size 14px q size 14px plus size 14px 3 size 14px p size 14px minus size 14px 3 end fraction$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Diketahui , maka Kemudian, diketahui sehingga Maka Jadi, jawaban yang tepat adalah E.

Diketahui $begin mathsize 14px style log presubscript presuperscript 2 invisible function application 10 equals fraction numerator 2 p over denominator p plus 1 end fraction end style$ , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 invisible function application 10 space end cell equals cell log presuperscript 2 invisible function application open parentheses 2 times 5 close parentheses end cell row cell fraction numerator 2 p over denominator p plus 1 end fraction end cell equals cell scriptbase log invisible function application 2 end scriptbase presuperscript 2 plus scriptbase log invisible function application 5 end scriptbase presuperscript 2 end cell row cell fraction numerator 2 p over denominator p plus 1 end fraction end cell equals cell 1 plus scriptbase log invisible function application 5 end scriptbase presuperscript 2 end cell row cell scriptbase log invisible function application 5 end scriptbase presuperscript 2 end cell equals cell fraction numerator 2 p over denominator p plus 1 end fraction minus 1 end cell row cell scriptbase log invisible function application 5 end scriptbase presuperscript 2 end cell equals cell fraction numerator 2 p minus p minus 1 over denominator p plus 1 end fraction end cell row cell scriptbase log invisible function application 5 end scriptbase presuperscript 2 end cell equals cell fraction numerator p minus 1 over denominator p plus 1 end fraction end cell row cell scriptbase log invisible function application 2 end scriptbase presuperscript 5 end cell equals cell fraction numerator p plus 1 over denominator p minus 1 end fraction end cell end table end style$

Kemudian, diketahui sehingga

Maka

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 minus scriptbase log invisible function application end scriptbase presuperscript 12 15 space end cell equals cell 2 minus fraction numerator scriptbase log invisible function application end scriptbase presuperscript 5 15 over denominator scriptbase log invisible function application end scriptbase presuperscript 5 12 end fraction end cell row blank equals cell 2 minus fraction numerator scriptbase log invisible function application end scriptbase presuperscript 5 open parentheses 3 times 5 close parentheses over denominator scriptbase log invisible function application end scriptbase presuperscript 5 open parentheses 2 squared times 3 close parentheses end fraction end cell row blank equals cell 2 minus fraction numerator scriptbase log invisible function application end scriptbase presuperscript 5 3 plus scriptbase log invisible function application end scriptbase presuperscript 5 5 over denominator scriptbase log invisible function application end scriptbase presuperscript 5 2 squared plus scriptbase log invisible function application end scriptbase presuperscript 5 3 end fraction end cell row blank equals cell 2 minus open parentheses fraction numerator begin display style 3 over q end style plus 1 over denominator 2 scriptbase log invisible function application end scriptbase presuperscript 5 2 plus begin display style 3 over q end style end fraction close parentheses end cell row blank equals cell 2 minus fraction numerator begin display style fraction numerator 3 plus q over denominator q end fraction end style over denominator 2 space open parentheses begin display style fraction numerator p plus 1 over denominator p minus 1 end fraction end style close parentheses plus begin display style 3 over q end style end fraction end cell row blank equals cell 2 minus fraction numerator begin display style fraction numerator 3 plus q over denominator q end fraction end style over denominator begin display style fraction numerator 2 p q plus 2 q plus 3 p minus 3 over denominator left parenthesis p minus 1 right parenthesis q end fraction end style end fraction end cell row blank equals cell 2 minus fraction numerator 3 p minus 3 plus p q minus q over denominator 2 p q plus 2 q plus 3 p minus 3 end fraction end cell row blank equals cell fraction numerator 4 p q plus 4 q plus 6 p minus 6 minus 3 p plus 3 minus p q plus q over denominator 2 p q plus 2 q plus 3 p minus 3 end fraction end cell row blank equals cell fraction numerator 3 p q plus 3 p plus 5 q minus 3 over denominator 2 p q plus 2 q plus 3 p minus 3 end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah E.