Solve for x 9^x=4

$9^{x} = 4$

Step 1

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

$\ln (9^{x}) = \ln (4)$

Step 2

Expand $\ln (9^{x})$ by moving $x$ outside the logarithm.

$x \ln (9) = \ln (4)$

Step 3

Divide each term in $x \ln (9) = \ln (4)$ by $\ln (9)$ and simplify.

Divide each term in $x \ln (9) = \ln (4)$ by $\ln (9)$ .

$\frac{x \ln (9)}{\ln (9)} = \frac{\ln (4)}{\ln (9)}$

Simplify the left side.

Cancel the common factor of $\ln (9)$ .

Cancel the common factor.

$\frac{x \ln (9)}{\ln (9)} = \frac{\ln (4)}{\ln (9)}$

Divide $x$ by $1$ .

$x = \frac{\ln (4)}{\ln (9)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (4)}{\ln (9)}$

Decimal Form:

$x = 0.63092975 \dots$