If $\log_{18} 24 = p$, then $\log_{96} 108$ equals

Question and options

\log_{18} 24 = p

, then

\log_{96} 108

equals

$\frac{p+2}{7p-3}$
$\frac{p+7}{9p-2}$
$\frac{3p+3}{3p+2}$
$\frac{3p+2}{3p+1}$

Answer and explanation

Correct answer: B - $\frac{p+7}{9p-2}$

Numerically p = log18(24) = 1.0995 and log96(108) = 1.0258; (p+7)/(9p-2) = 1.0258 matches, others do not. Algebraically with log2=u, log3=w: p = (3u+w)/(u+2w), and (p+7)/(9p-2) = (2u+3w)/(5u+w) = log108/log96.

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If \(\log_{18} 24 = p\), then \(\log_{96} 108\) equals