Solve the Inequality for x 4^x<=36

$4^{x} \leq 36$

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

$\ln (4^{x}) \leq \ln (36)$

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

$x \ln (4) \leq \ln (36)$

Divide each term in $x \ln (4) \leq \ln (36)$ by $\ln (4)$ and simplify.

Divide each term in $x \ln (4) \leq \ln (36)$ by $\ln (4)$ .

$\frac{x \ln (4)}{\ln (4)} \leq \frac{\ln (36)}{\ln (4)}$

Simplify the left side.

Cancel the common factor of $\ln (4)$ .

Cancel the common factor.

$\frac{x \ln (4)}{\ln (4)} \leq \frac{\ln (36)}{\ln (4)}$

Divide $x$ by $1$ .

$x \leq \frac{\ln (36)}{\ln (4)}$

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{\ln (36)}{\ln (4)}$

Interval Notation:

$(- \infty, \frac{\ln (36)}{\ln (4)}]$