Solve for x b^x=n

$b^{x} = n$

Step 1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (b^{x}) = \ln (n)$

Step 2

Expand $\ln (b^{x})$ by moving $x$ outside the logarithm.

$x \ln (b) = \ln (n)$

Step 3

Divide each term in $x \ln (b) = \ln (n)$ by $\ln (b)$ and simplify.

Divide each term in $x \ln (b) = \ln (n)$ by $\ln (b)$ .

$\frac{x \ln (b)}{\ln (b)} = \frac{\ln (n)}{\ln (b)}$

Simplify the left side.

Cancel the common factor of $\ln (b)$ .

Cancel the common factor.

$\frac{x \ln (b)}{\ln (b)} = \frac{\ln (n)}{\ln (b)}$

Divide $x$ by $1$ .

$x = \frac{\ln (n)}{\ln (b)}$