Precalculus Examples

$2 \log (- 2 y^{- 1})$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 \log (- 2 \frac{1}{y})$

Step 2

Combine $- 2$ and $\frac{1}{y}$ .

$2 \log (\frac{- 2}{y})$

Step 3

Move the negative in front of the fraction.

$2 \log (- \frac{2}{y})$

Step 4

Simplify $2 \log (- \frac{2}{y})$ by moving $2$ inside the logarithm.

$\log ({(- \frac{2}{y})}^{2})$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 5.1

Apply the product rule to $- \frac{2}{y}$ .

$\log ({(- 1)}^{2} {(\frac{2}{y})}^{2})$

Step 5.2

Apply the product rule to $\frac{2}{y}$ .

$\log ({(- 1)}^{2} \frac{2^{2}}{y^{2}})$

Step 6

Raise $- 1$ to the power of $2$ .

$\log (1 \frac{2^{2}}{y^{2}})$

Step 7

Multiply $\frac{2^{2}}{y^{2}}$ by $1$ .

$\log (\frac{2^{2}}{y^{2}})$

Step 8

Raise $2$ to the power of $2$ .

$\log (\frac{4}{y^{2}})$