Solve for x 5^(3x)=15

$5^{3 x} = 15$

Step 1

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

$\ln (5^{3 x}) = \ln (15)$

Step 2

Expand $\ln (5^{3 x})$ by moving $3 x$ outside the logarithm.

$3 x \ln (5) = \ln (15)$

Step 3

Divide each term in $3 x \ln (5) = \ln (15)$ by $3 \ln (5)$ and simplify.

Divide each term in $3 x \ln (5) = \ln (15)$ by $3 \ln (5)$ .

$\frac{3 x \ln (5)}{3 \ln (5)} = \frac{\ln (15)}{3 \ln (5)}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x \ln (5)}{3 \ln (5)} = \frac{\ln (15)}{3 \ln (5)}$

Rewrite the expression.

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (15)}{3 \ln (5)}$

Cancel the common factor of $\ln (5)$ .

Cancel the common factor.

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (15)}{3 \ln (5)}$

Divide $x$ by $1$ .

$x = \frac{\ln (15)}{3 \ln (5)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (15)}{3 \ln (5)}$

Decimal Form:

$x = 0.56086873 \dots$