Solve for x 3^(2x)=30

$3^{2 x} = 30$

Step 1

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

$\ln (3^{2 x}) = \ln (30)$

Step 2

Expand $\ln (3^{2 x})$ by moving $2 x$ outside the logarithm.

$2 x \ln (3) = \ln (30)$

Step 3

Divide each term in $2 x \ln (3) = \ln (30)$ by $2 \ln (3)$ and simplify.

Divide each term in $2 x \ln (3) = \ln (30)$ by $2 \ln (3)$ .

$\frac{2 x \ln (3)}{2 \ln (3)} = \frac{\ln (30)}{2 \ln (3)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x \ln (3)}{2 \ln (3)} = \frac{\ln (30)}{2 \ln (3)}$

Rewrite the expression.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (30)}{2 \ln (3)}$

Cancel the common factor of $\ln (3)$ .

Cancel the common factor.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (30)}{2 \ln (3)}$

Divide $x$ by $1$ .

$x = \frac{\ln (30)}{2 \ln (3)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (30)}{2 \ln (3)}$

Decimal Form:

$x = 1.54795163 \dots$