Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 143965 by Khalmohmmad last updated on 20/Jun/21

Commented by Canebulok last updated on 20/Jun/21

$$\mathit{S}\mathit{o}\mathit{l}\mathit{u}\mathit{t}\mathit{i}\mathit{o}\mathit{n}:$$$$\Rightarrow \frac{log\left(x\right)}{log\left(3\right)}+\frac{log\left(5\right)}{log\left(x\right)}=0$$$$\Rightarrow log{\left(x\right)}^2+log\left(5\right)log\left(3\right)=0$$$$$$$$Let:k=log\left(x\right)$$$$\Rightarrow k^2+log\left(5\right)log\left(3\right)=0$$$$Byusingthequadraticformula:$$$$\Rightarrow k=\frac{\pm \sqrt{-4\left(log\left(3\right)log\left(5\right)\right)}}{2}$$$$\Rightarrow k_1=+i\sqrt{log\left(3\right)log\left(5\right)}$$$$\Rightarrow k_2=-i\sqrt{log\left(3\right)log\left(5\right)}$$$$$$$$Thus;$$$$\Rightarrow log\left(x\right)=\pm i\sqrt{log\left(3\right)log\left(5\right)}$$$$\Rightarrow x={10}^{\pm i\sqrt{log\left(3\right)log\left(5\right)}}$$$$$$$$\sim Kevin$$

Answered by mr W last updated on 20/Jun/21

$$\frac{\ln x}{\ln 3}+\frac{\ln 5}{\ln x}=0$$$$\ln x=\pm i\sqrt{\ln 3\ln 5}$$$$x=e^{\pm i\sqrt{\ln 3\ln 5}}=\cos \sqrt{\ln 3\ln 5}\pm i\sin \sqrt{\ln 3\ln 5}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com