Solve for x 17^x=89

$17^{x} = 89$

Step 1

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

$\ln (17^{x}) = \ln (89)$

Step 2

Expand $\ln (17^{x})$ by moving $x$ outside the logarithm.

$x \ln (17) = \ln (89)$

Step 3

Divide each term in $x \ln (17) = \ln (89)$ by $\ln (17)$ and simplify.

Divide each term in $x \ln (17) = \ln (89)$ by $\ln (17)$ .

$\frac{x \ln (17)}{\ln (17)} = \frac{\ln (89)}{\ln (17)}$

Simplify the left side.

Cancel the common factor of $\ln (17)$ .

Cancel the common factor.

$\frac{x \ln (17)}{\ln (17)} = \frac{\ln (89)}{\ln (17)}$

Divide $x$ by $1$ .

$x = \frac{\ln (89)}{\ln (17)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (89)}{\ln (17)}$

Decimal Form:

$x = 1.58429169 \dots$