Jika diketahui 2log 3 =p dan 3log5 =q, maka nilai dari 6log 45 adalah ....

Pertanyaan

Jika diketahui $\style{font-size:14px}{\;^2\log\;3\;=\mathrm p\;\mathrm{dan}\;^3\log5\;=\mathrm q,\;\mathrm{maka}\;\mathrm{nilai}\;\mathrm{dari}\;^6\log\;45}$ adalah ....

$fraction numerator 2 straight p plus pq over denominator 1 minus straight p end fraction$
$fraction numerator 2 straight p minus pq over denominator 1 plus straight p end fraction$
$fraction numerator 2 straight p plus pq over denominator 1 plus straight p end fraction$
$fraction numerator straight p minus 2 pq over denominator 1 plus straight p end fraction$
$fraction numerator straight p plus 2 pq over denominator 1 plus straight p end fraction$

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style blank squared log 3 equals straight p left right double arrow fraction numerator log 3 over denominator log 2 end fraction equals straight p left right double arrow log 2 equals 1 over straight p log 3 to the power of space 3 end exponent log 5 equals straight p left right double arrow fraction numerator log 5 over denominator log 3 end fraction equals straight q left right double arrow log 5 equals qlog 3 to the power of space 6 end exponent log 45 equals fraction numerator log 45 over denominator log 6 end fraction space space space space space space space space space space equals fraction numerator log left parenthesis 3 squared space straight x space 5 right parenthesis over denominator log left parenthesis 3 space straight x space 2 right parenthesis end fraction space space space space space space space space space space equals fraction numerator log 3 squared plus log 5 over denominator log 3 space plus log 2 end fraction space space space space space space space space space space equals fraction numerator 2 log 3 plus log 5 over denominator log 3 space plus log 2 end fraction space space space space space space space space space space equals fraction numerator 2 log 3 plus qlog 3 over denominator log 3 space plus begin display style 1 over straight p end style log 3 end fraction space space space space space space space space space space equals fraction numerator left parenthesis 2 plus straight q right parenthesis up diagonal strike log 3 end strike over denominator open parentheses 1 plus begin display style 1 over straight p end style close parentheses up diagonal strike log 3 end strike end fraction equals fraction numerator 2 plus straight q over denominator 1 end fraction straight x fraction numerator straight p over denominator 1 plus straight p end fraction equals fraction numerator 2 straight p plus pq over denominator 1 plus straight p end fraction end style$

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