Solve for x 9^x>54

$9^{x} > 54$

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

$\ln (9^{x}) > \ln (54)$

Expand $\ln (9^{x})$ by moving $x$ outside the logarithm.

$x \ln (9) > \ln (54)$

Divide each term in $x \ln (9) > \ln (54)$ by $\ln (9)$ and simplify.

Divide each term in $x \ln (9) > \ln (54)$ by $\ln (9)$ .

$\frac{x \ln (9)}{\ln (9)} > \frac{\ln (54)}{\ln (9)}$

Simplify the left side.

Cancel the common factor of $\ln (9)$ .

Cancel the common factor.

$\frac{x \ln (9)}{\ln (9)} > \frac{\ln (54)}{\ln (9)}$

Divide $x$ by $1$ .

$x > \frac{\ln (54)}{\ln (9)}$

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{\ln (54)}{\ln (9)}$

Interval Notation:

$(\frac{\ln (54)}{\ln (9)}, \infty)$