Solve for x 11^(5x)=33

$11^{5 x} = 33$

Step 1

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

$\ln (11^{5 x}) = \ln (33)$

Step 2

Expand $\ln (11^{5 x})$ by moving $5 x$ outside the logarithm.

$5 x \ln (11) = \ln (33)$

Step 3

Divide each term in $5 x \ln (11) = \ln (33)$ by $5 \ln (11)$ and simplify.

Divide each term in $5 x \ln (11) = \ln (33)$ by $5 \ln (11)$ .

$\frac{5 x \ln (11)}{5 \ln (11)} = \frac{\ln (33)}{5 \ln (11)}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x \ln (11)}{5 \ln (11)} = \frac{\ln (33)}{5 \ln (11)}$

Rewrite the expression.

$\frac{x \ln (11)}{\ln (11)} = \frac{\ln (33)}{5 \ln (11)}$

Cancel the common factor of $\ln (11)$ .

Cancel the common factor.

$\frac{x \ln (11)}{\ln (11)} = \frac{\ln (33)}{5 \ln (11)}$

Divide $x$ by $1$ .

$x = \frac{\ln (33)}{5 \ln (11)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (33)}{5 \ln (11)}$

Decimal Form:

$x = 0.29163138 \dots$