Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 211099 by peter frank last updated on 27/Aug/24

Answered by A5T last updated on 27/Aug/24

$$2^{logx}=2^{\frac{{log}_{2}x}{{log}_{2}10}}=x^{\frac{1}{{log}_{2}10}}=x^{{log}_{10}2}=\frac{x}{25}$$$$\Rightarrow x^{1-log2}=25\Rightarrow x={25}^{\frac{1}{1og5}}={25}^{{log}_{5}10}={\left(5^{{log}_{5}10}\right)}^2$$$$\Rightarrow x={10}^2=100$$

Commented by peter frank last updated on 28/Aug/24

$$\mathrm{thank}\mathrm{you}$$

Answered by mr W last updated on 27/Aug/24

$$\left(\log 2\right)\log x=\log x-\log 25$$$$(1-\log 2)\log x=\log 25$$$$\log x=\frac{\log 25}{1-\log 2}=\frac{2\log 5}{\log 5}=2$$$$\Rightarrow x={10}^2=100$$

Commented by peter frank last updated on 28/Aug/24

$$\mathrm{thank}\mathrm{you}$$

Answered by mm1342 last updated on 27/Aug/24

$$logx\times log2=logx-log25$$$$\Rightarrow logx(1-log2)=log25$$$$\Rightarrow logx=\frac{log25}{log5}=2\Rightarrow x=100✓$$$$$$

Commented by peter frank last updated on 28/Aug/24

$$\mathrm{thank}\mathrm{you}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com