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Question Number 96289 by rb222 last updated on 31/May/20

$${1010}^x+{2020}^x={4040}^x$$$$x=?$$

Commented by bobhans last updated on 31/May/20

$${\left(\frac{1}{4}\right)}^x+{\left(\frac{1}{2}\right)}^x=1[\mathrm{t}={\left(\frac{1}{2}\right)}^x]$$$$t^2+t-1=0\Rightarrow \mathrm{t}=\frac{-1+\sqrt{5}}{2}$$$$-x\ln \left(2\right)=\ln (\sqrt{5}-1)-\ln \left(2\right)$$$$x=\frac{\ln \left(2\right)-\ln (\sqrt{5}-1)}{\ln \left(2\right)}$$

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