If-log-12-18-a-find-log-24-16-in-term-of-a-

Question Number 34301 by math1967 last updated on 03/May/18

I f {l o g}_{12} 18 = a, f i n d {l o g}_{24} 16 i n t e r m

o f a

Answered by MJS last updated on 03/May/18

12^{a} = 18

a = \frac{\ln 18}{2 \ln 2 + \ln 3}

\frac{\ln 18}{a} = 2 \ln 2 + \ln 3

24^{b} = 16

b = \frac{\ln 16}{3 \ln 2 + \ln 3}

\frac{\ln 16}{b} = 3 \ln 2 + \ln 3

\frac{\ln 16}{b} = \frac{\ln 18 + a \ln 2}{a}

b = \frac{a \ln 16}{\ln 18 + a \ln 2}

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