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Question Number 210034 by peter frank last updated on 29/Jul/24

Commented by peter frank last updated on 29/Jul/24

$$\mathrm{solve}\mathrm{for}\mathrm{x}$$

Commented by Frix last updated on 29/Jul/24

$${\left(\log 5\right)}^{\log x}\mathrm{or}\log \left(5^{\log x}\right)?$$$$\log =\ln \mathrm{or}\log ={\log }_{10}?$$

Commented by peter frank last updated on 29/Jul/24

$$\log \left(5^{\mathrm{logx}}\right)$$

Commented by Frix last updated on 29/Jul/24

$$\log \left(5^{\log x}\right)=\log x\times \log 5$$$$\mathrm{For}\mathrm{the}\mathrm{base}b:$$$${\log }_{b}x\frac{4}{{\log }_{b}5}$$$$x=b^{\frac{4}{{\log }_{b}5}}$$$$b=10\Rightarrow x={10}^{\frac{4}{{\log }_{10}5}}\approx 528087.919$$$$b=\mathrm{e}\Rightarrow x={\mathrm{e}}^{\frac{4}{\ln 5}}\approx 12.0051983$$

Answered by Spillover last updated on 29/Jul/24

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