Solve for x 50^x=0.02

$50^{x} = 0.02$

Step 1

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

$\ln (50^{x}) = \ln (0.02)$

Step 2

Expand $\ln (50^{x})$ by moving $x$ outside the logarithm.

$x \ln (50) = \ln (0.02)$

Step 3

Divide each term in $x \ln (50) = \ln (0.02)$ by $\ln (50)$ and simplify.

Divide each term in $x \ln (50) = \ln (0.02)$ by $\ln (50)$ .

$\frac{x \ln (50)}{\ln (50)} = \frac{\ln (0.02)}{\ln (50)}$

Simplify the left side.

Cancel the common factor of $\ln (50)$ .

Cancel the common factor.

$\frac{x \ln (50)}{\ln (50)} = \frac{\ln (0.02)}{\ln (50)}$

Divide $x$ by $1$ .

$x = \frac{\ln (0.02)}{\ln (50)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (0.02)}{\ln (50)}$

Decimal Form:

$x = - 1$