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

$$If{log}_{12}18=a,find{log}_{24}16interm$$$$ofa$$

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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