Solve for x 15^(2x)=36

$15^{2 x} = 36$

Step 1

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

$\ln (15^{2 x}) = \ln (36)$

Step 2

Expand $\ln (15^{2 x})$ by moving $2 x$ outside the logarithm.

$2 x \ln (15) = \ln (36)$

Step 3

Divide each term in $2 x \ln (15) = \ln (36)$ by $2 \ln (15)$ and simplify.

Divide each term in $2 x \ln (15) = \ln (36)$ by $2 \ln (15)$ .

$\frac{2 x \ln (15)}{2 \ln (15)} = \frac{\ln (36)}{2 \ln (15)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x \ln (15)}{2 \ln (15)} = \frac{\ln (36)}{2 \ln (15)}$

Rewrite the expression.

$\frac{x \ln (15)}{\ln (15)} = \frac{\ln (36)}{2 \ln (15)}$

Cancel the common factor of $\ln (15)$ .

Cancel the common factor.

$\frac{x \ln (15)}{\ln (15)} = \frac{\ln (36)}{2 \ln (15)}$

Divide $x$ by $1$ .

$x = \frac{\ln (36)}{2 \ln (15)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (36)}{2 \ln (15)}$

Decimal Form:

$x = 0.66164189 \dots$