Solve the Inequality for x 6^x>12

$6^{x} > 12$

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

$\ln (6^{x}) > \ln (12)$

Expand $\ln (6^{x})$ by moving $x$ outside the logarithm.

$x \ln (6) > \ln (12)$

Divide each term in $x \ln (6) > \ln (12)$ by $\ln (6)$ and simplify.

Divide each term in $x \ln (6) > \ln (12)$ by $\ln (6)$ .

$\frac{x \ln (6)}{\ln (6)} > \frac{\ln (12)}{\ln (6)}$

Simplify the left side.

Cancel the common factor of $\ln (6)$ .

Cancel the common factor.

$\frac{x \ln (6)}{\ln (6)} > \frac{\ln (12)}{\ln (6)}$

Divide $x$ by $1$ .

$x > \frac{\ln (12)}{\ln (6)}$

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{\ln (12)}{\ln (6)}$

Interval Notation:

$(\frac{\ln (12)}{\ln (6)}, \infty)$