Solve for x 16^x=0.5

$16^{x} = 0.5$

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

$\ln (16^{x}) = \ln (0.5)$

Expand $\ln (16^{x})$ by moving $x$ outside the logarithm.

$x \ln (16) = \ln (0.5)$

Divide each term in $x \ln (16) = \ln (0.5)$ by $\ln (16)$ and simplify.

Divide each term in $x \ln (16) = \ln (0.5)$ by $\ln (16)$ .

$\frac{x \ln (16)}{\ln (16)} = \frac{\ln (0.5)}{\ln (16)}$

Simplify the left side.

Cancel the common factor of $\ln (16)$ .

Cancel the common factor.

$\frac{x \ln (16)}{\ln (16)} = \frac{\ln (0.5)}{\ln (16)}$

Divide $x$ by $1$ .

$x = \frac{\ln (0.5)}{\ln (16)}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (0.5)}{\ln (16)}$

Decimal Form:

$x = - 0.25$