Solve for x 20^x=0.05

$20^{x} = 0.05$

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

$\ln (20^{x}) = \ln (0.05)$

Expand $\ln (20^{x})$ by moving $x$ outside the logarithm.

$x \ln (20) = \ln (0.05)$

Divide each term in $x \ln (20) = \ln (0.05)$ by $\ln (20)$ and simplify.

Divide each term in $x \ln (20) = \ln (0.05)$ by $\ln (20)$ .

$\frac{x \ln (20)}{\ln (20)} = \frac{\ln (0.05)}{\ln (20)}$

Simplify the left side.

Cancel the common factor of $\ln (20)$ .

Cancel the common factor.

$\frac{x \ln (20)}{\ln (20)} = \frac{\ln (0.05)}{\ln (20)}$

Divide $x$ by $1$ .

$x = \frac{\ln (0.05)}{\ln (20)}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (0.05)}{\ln (20)}$

Decimal Form:

$x = - 1$