Calculus Examples

$\log_{b} ({(2 b)}^{- 5})$

Step 1

Expand $\log_{b} ({(2 b)}^{- 5})$ by moving $- 5$ outside the logarithm.

$- 5 \log_{b} (2 b)$

Step 2

Rewrite $\log_{b} (2 b)$ as $\log_{b} (2) + \log_{b} (b)$ .

$- 5 (\log_{b} (2) + \log_{b} (b))$

Step 3

Logarithm base $b$ of $b$ is $1$ .

$- 5 (\log_{b} (2) + 1)$

Step 4

Apply the distributive property.

$- 5 \log_{b} (2) - 5 \cdot 1$

Step 5

Multiply $- 5$ by $1$ .

$- 5 \log_{b} (2) - 5$