Jika 3log 5 = A, dan 5log 2 = B, maka nilai 12log 15 adalah ?.... Question from @Heldaaa

IcukSugiarto $\bold{\underline{Solution:}}\\\\~^{3}\log\ 5=A\\~^{5}\log\ 2=B\\\\sehingga:\\\displaystyle~^{12}\log\ 15\\\\= \frac{~^{5}\log\ 15}{~^{5}\log\ 12}\\\\= \frac{~^{5}\log\ (3\times 5)}{~^{5}\log\ (3\times 4)} \\\\= \frac{~^{5}\log\ 3+~^{5}\log\ 5}{~^{5}\log\ 3+~^{5}\log\ 4}$

$\\\\\displaystyle= \frac{ \frac{1}{~^{3}\log\ 5} +~^{5}\log\ 5}{\frac{1}{~^{3}\log\ 5}+~^{5}\log\ 2^{2}}\\\\\\= \frac{ \frac{1}{~^{3}\log\ 5} +~^{5}\log\ 5}{\frac{1}{~^{3}\log\ 5}+2~^{5}\log\ 2}\\\\\\= \frac{ \frac{1}{A} +1}{\frac{1}{A}+2B}\\\\\\= \frac{ \frac{1}{A} +1}{\frac{1}{A}+2B}\times \frac{A}{A}$

$\\\\\displaystyle= \frac{1 +A}{1+2AB}$

subebe 12 log 15 = 5log 15 / 5log 12
   = 5log (3x5) / 5log (2x2x3)
   = (5log 3 + 5log5) / (5log2 + 5log2 + 5log3)
   = (1/A + 1) / (B + B + 1/A)
   = ( (1+A)/A) / ((2AB +1)/A)
   = (1+A) / (2AB + 1)

Jika 2log 5 = a, maka 8log 125 + 2log 10 adalah ?

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