Precalculus Examples

$y = 10 \log (\frac{1}{10^{- 12}})$

Step 1

Divide both sides by $10$ to remove it from the front of the logarithm.

$\frac{y}{10} = \frac{10 \log (\frac{1}{10^{- 12}})}{10}$

Step 2

Simplify each side of the equation.

$\frac{y}{10} = \log (\frac{1}{10^{- 12}})$

Step 3

For logarithmic equations, $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ such that $x > 0$ , $b > 0$ , and $b \neq 1$ . In this case, $b = 10$ , $x = \frac{1}{10^{- 12}}$ , and $y = \frac{y}{10}$ .

$b = 10$

$x = \frac{1}{10^{- 12}}$

$y = \frac{y}{10}$

Step 4

Substitute the values of $b$ , $x$ , and $y$ into the equation $b^{y} = x$ .

$10^{\frac{y}{10}} = \frac{1}{10^{- 12}}$