Solve for b 3^b=17

$3^{b} = 17$

Step 1

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

$\ln (3^{b}) = \ln (17)$

Step 2

Expand $\ln (3^{b})$ by moving $b$ outside the logarithm.

$b \ln (3) = \ln (17)$

Step 3

Divide each term in $b \ln (3) = \ln (17)$ by $\ln (3)$ and simplify.

Divide each term in $b \ln (3) = \ln (17)$ by $\ln (3)$ .

$\frac{b \ln (3)}{\ln (3)} = \frac{\ln (17)}{\ln (3)}$

Simplify the left side.

Cancel the common factor of $\ln (3)$ .

Cancel the common factor.

$\frac{b \ln (3)}{\ln (3)} = \frac{\ln (17)}{\ln (3)}$

Divide $b$ by $1$ .

$b = \frac{\ln (17)}{\ln (3)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$b = \frac{\ln (17)}{\ln (3)}$

Decimal Form:

$b = 2.57890192 \dots$