Solve for y 3^y=1

$3^{y} = 1$

Step 1

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

$\ln (3^{y}) = \ln (1)$

Step 2

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

$y \ln (3) = \ln (1)$

Step 3

Simplify the right side.

The natural logarithm of $1$ is $0$ .

$y \ln (3) = 0$

Step 4

Divide each term in $y \ln (3) = 0$ by $\ln (3)$ and simplify.

Divide each term in $y \ln (3) = 0$ by $\ln (3)$ .

$\frac{y \ln (3)}{\ln (3)} = \frac{0}{\ln (3)}$

Simplify the left side.

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

Cancel the common factor.

$\frac{y \ln (3)}{\ln (3)} = \frac{0}{\ln (3)}$

Divide $y$ by $1$ .

$y = \frac{0}{\ln (3)}$

Simplify the right side.

Divide $0$ by $\ln (3)$ .

$y = 0$