Solve for x 12^(4x)=7

$12^{4 x} = 7$

Step 1

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

$\ln (12^{4 x}) = \ln (7)$

Step 2

Expand $\ln (12^{4 x})$ by moving $4 x$ outside the logarithm.

$4 x \ln (12) = \ln (7)$

Step 3

Divide each term in $4 x \ln (12) = \ln (7)$ by $4 \ln (12)$ and simplify.

Divide each term in $4 x \ln (12) = \ln (7)$ by $4 \ln (12)$ .

$\frac{4 x \ln (12)}{4 \ln (12)} = \frac{\ln (7)}{4 \ln (12)}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x \ln (12)}{4 \ln (12)} = \frac{\ln (7)}{4 \ln (12)}$

Rewrite the expression.

$\frac{x \ln (12)}{\ln (12)} = \frac{\ln (7)}{4 \ln (12)}$

Cancel the common factor of $\ln (12)$ .

Cancel the common factor.

$\frac{x \ln (12)}{\ln (12)} = \frac{\ln (7)}{4 \ln (12)}$

Divide $x$ by $1$ .

$x = \frac{\ln (7)}{4 \ln (12)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (7)}{4 \ln (12)}$

Decimal Form:

$x = 0.19577296 \dots$