[กิตติ]

$\frac{log{12}}{log{15}} =k $
$12=15^k$
$\frac{log{12}+log{15}}{log{15}} =k+1$
$\frac{log{(12\times 15)}}{log{15}} =k+1$
$\frac{log{\frac{4}{75}}}{log{15}}=k-2$
$\frac{log{(12\times 15)}}{log{\frac{4}{75}}} =\frac{k+1}{k-2} $

ติดแหง็กตรงค่าของ $log(12\times 15)$
$log(12\times 15)=2log2+2log3+log5$
$=2-2log5+2log3+log5$
$=2+2log3-log5$
$=1+2log3+log2$

$\frac{log{12}}{log{15}} =k $
$2log2+log3=klog5+klog3$
$2log2+log3=k-klog2+klog3$
$log2(k+2)=(k-1)log3$

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