Solve for y 12^y=22

$12^{y} = 22$

Step 1

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

$\ln (12^{y}) = \ln (22)$

Step 2

Expand $\ln (12^{y})$ by moving $y$ outside the logarithm.

$y \ln (12) = \ln (22)$

Step 3

Divide each term in $y \ln (12) = \ln (22)$ by $\ln (12)$ and simplify.

Divide each term in $y \ln (12) = \ln (22)$ by $\ln (12)$ .

$\frac{y \ln (12)}{\ln (12)} = \frac{\ln (22)}{\ln (12)}$

Simplify the left side.

Cancel the common factor of $\ln (12)$ .

Cancel the common factor.

$\frac{y \ln (12)}{\ln (12)} = \frac{\ln (22)}{\ln (12)}$

Divide $y$ by $1$ .

$y = \frac{\ln (22)}{\ln (12)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{\ln (22)}{\ln (12)}$

Decimal Form:

$y = 1.24392699 \dots$