Precalculus Examples

$10 \log (\frac{x}{10^{- 16}})$

Step 1

Rewrite $\frac{x}{10^{- 16}}$ as $x {(10^{- 16})}^{- 1}$ .

$10 \log (x {(10^{- 16})}^{- 1})$

Step 2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10 \log (x \cdot 10^{- 16 \cdot - 1})$

Step 3

Rewrite $\log (x \cdot 10^{- 16 \cdot - 1})$ as $\log (x) + \log (10^{- 16 \cdot - 1})$ .

$10 (\log (x) + \log (10^{- 16 \cdot - 1}))$

Step 4

Use logarithm rules to move $- 16 \cdot - 1$ out of the exponent.

$10 (\log (x) - 16 \cdot - 1 \log (10))$

Step 5

Multiply $- 16$ by $- 1$ .

$10 (\log (x) + 16 \log (10))$

Step 6

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

$10 (\log (x) + 16 \cdot 1)$

Step 7

Multiply $16$ by $1$ .

$10 (\log (x) + 16)$

Step 8

Apply the distributive property.

$10 \log (x) + 10 \cdot 16$

Step 9

Simplify $10 \log (x)$ by moving $10$ inside the logarithm.

$\log (x^{10}) + 10 \cdot 16$

Step 10

Multiply $10$ by $16$ .

$\log (x^{10}) + 160$