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Question Number 170669 by solomonwells last updated on 28/May/22

Commented by kaivan.ahmadi last updated on 28/May/22

$$y={log}_{6}x\Rightarrow x=6^y$$$$6^{y^2}+{\left(6^y\right)}^y=12\Rightarrow 2\times 6^{y^2}=12\Rightarrow 6^{y^2}=6\Rightarrow$$$$y^2=1\Rightarrow y=\pm 1$$$$ify=1\Rightarrow {log}_{6}x=1\Rightarrow x=6$$$$ify=-1\Rightarrow {log}_{6}x=-1\Rightarrow x=6^{-1}=\frac{1}{6}$$

Commented by solomonwells last updated on 28/May/22

$$\mathit{i}\mathit{r}\mathit{e}\mathit{a}\mathit{l}\mathit{l}\mathit{y}\mathit{a}\mathit{p}\mathit{p}\mathit{r}\mathit{e}\mathit{c}\mathit{i}\mathit{a}\mathit{t}\mathit{e}\mathit{t}\mathit{h}\mathit{i}\mathit{s}\mathit{s}\mathit{i}\mathit{r}$$

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