# How do you solve log_2 x=log_5 3?

$x = {2}^{\ln \frac{3}{\ln} \left(5\right)} \approx 1.605$
By the change of base formula ${\log}_{5} \left(3\right) = \ln \frac{3}{\ln} \left(5\right)$
Then $x = {2}^{{\log}_{2} x} = {2}^{{\log}_{5} \left(3\right)} = {2}^{\ln \frac{3}{\ln} \left(5\right)}$