How do you solve log_2x=log_5 3?

May 26, 2016

$x = 1.605$

Explanation:

${\log}_{2} x = {\log}_{53}$ can be simplified using ${\log}_{b} a = \log \frac{a}{\log} b$. Hence it is

$\log \frac{x}{\log} 2 = \log \frac{3}{\log} 5$

or $\log x = \log \frac{3}{\log} 5 \times \log 2$

or $\log x = \frac{0.4771}{0.6990} \times 0.3010$

Hence $x = {10}^{\frac{0.4771}{0.6990} \times 0.3010} = 1.605$