Answer
$x = \dfrac{\ln{10}}{\ln{2}}\approx 3.322$
Work Step by Step
Take the natural logarithm of both sides to obtain:
$\ln{2^x} = \ln{10}$
Use the rule $\ln{a^x} = x \cdot \ln{a}$ to obtain:
$x\cdot \ln{2} = \ln{10}$
Divide both sides of the equation by $\ln{2}$ to obtain:
$\dfrac{x\cdot \ln{2}}{\ln{2}}=\dfrac{\ln{10}}{\ln{2}}
\\x = \dfrac{\ln{10}}{\ln{2}}
\\x \approx 3.322$
