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Question Number 198050 by akolade last updated on 09/Oct/23

Answered by mr W last updated on 10/Oct/23

$$2^x=3^y=k,say$$$$\Rightarrow x=\frac{\log k}{\log 2},y=\frac{\log k}{\log 3}$$$$\frac{2\times \log 2+3\times \log 3}{\log k}=1$$$$\log k=\log 2^2\times 3^3=\log 108$$$$\Rightarrow k=108$$$$2^x+3^y=2k=216✓$$

Commented by necx122 last updated on 09/Oct/23

$$Mygoodness.Theapproachisreally$$$$cool.$$

Commented by akolade last updated on 10/Oct/23

$$\mathrm{wow}\mathrm{this}\mathrm{is}\mathrm{the}\mathrm{best}\mathrm{approach}\mathrm{i}\mathrm{have}\mathrm{seen}\mathrm{so}\mathrm{far}$$

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