Solve for y 10^y=1

$10^{y} = 1$

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{y}) = \log (1)$

Expand the left side.

Expand $\log (10^{y})$ by moving $y$ outside the logarithm.

$y \log (10) = \log (1)$

Logarithm base $10$ of $10$ is $1$ .

$y \cdot 1 = \log (1)$

Multiply $y$ by $1$ .

$y = \log (1)$

Logarithm base $10$ of $1$ is $0$ .

$y = 0$