Solve for x 4^x=5

$4^{x} = 5$

Step 1

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

$\ln (4^{x}) = \ln (5)$

Step 2

Expand $\ln (4^{x})$ by moving $x$ outside the logarithm.

$x \ln (4) = \ln (5)$

Step 3

Divide each term in $x \ln (4) = \ln (5)$ by $\ln (4)$ and simplify.

Divide each term in $x \ln (4) = \ln (5)$ by $\ln (4)$ .

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (5)}{\ln (4)}$

Simplify the left side.

Cancel the common factor of $\ln (4)$ .

Cancel the common factor.

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (5)}{\ln (4)}$

Divide $x$ by $1$ .

$x = \frac{\ln (5)}{\ln (4)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (5)}{\ln (4)}$

Decimal Form:

$x = 1.16096404 \dots$