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 21342 by xxyy@gmail.com last updated on 21/Sep/17

Answered by $@ty@m last updated on 23/Sep/17

$$Let10+{\log }_{10}{\left(x\right)}^{10+{\log }_{10}{\left(x\right)}^{10+....}}=y$$$$\Rightarrow 10+\log {}_{10}{x}^y=y--\left(1\right)$$$$\Rightarrow \log {}_{10}{x}^y=y-10$$$$\Rightarrow y\log {}_{10}x=y-10$$$$\Rightarrow \log {}_{10}x=\frac{y-10}{y}$$$$\Rightarrow \frac{1}{\log {}_{10}x}=\frac{y}{y-10}$$$$\Rightarrow \frac{1}{\log {}_{10}x}=\frac{10+\log x^y}{\log x^y},using\left(1\right)$$$$\Rightarrow \frac{1}{\log {}_{10}x}=1+\frac{10}{\log x^y}--\left(2\right)$$$$ATQ,$$$$1+x^y=\frac{1}{\log {}_{10}x}--\left(3\right)$$$$from\left(2\right)\mathrm{\&}\left(3\right),$$$$x^y=\frac{10}{\log x^y}$$$$\log {\left(x^y\right)}^{x^y}=10$$$${\left(x^y\right)}^{x^y}={10}^{10}$$$$x^y=10$$$$1+x^y=11$$$$\frac{1}{{\log }_{10}x}=11,from\left(3\right)$$$${\log }_{10}x=\frac{1}{11}$$$$x={10}^{\frac{1}{11}}Ans.$$$$$$

Commented by xxyy@gmail.com last updated on 23/Sep/17

$$\mathrm{thank}\mathrm{very}\mathrm{much}\mathrm{sir}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com