# How do you solve for the power of x? For example, 2^x = 423. How do you get x?

Oct 2, 2014

${2}^{x} = 423$

Take the natural log of both sides

$\ln \left({2}^{x}\right) = \ln \left(423\right)$

Use one of properties of logs to move the exponent down as a factor

$x \cdot \ln \left(2\right) = \ln \left(423\right)$

Use Algebra to solve for $x$ by dividing by $\ln \left(x\right)$

$\frac{x \cdot \ln \left(2\right)}{\ln \left(2\right)} = \ln \frac{423}{\ln \left(2\right)}$

Use a calculator to resolve the division

$x = \ln \frac{423}{\ln \left(2\right)} = 8.724513853$