Precalculus Examples

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

Step 1

Rewrite $\log (\frac{a}{10^{- 16}})$ as $\log (a) - \log (10^{- 16})$ .

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

Step 2

Expand $\log (10^{- 16})$ by moving $- 16$ outside the logarithm.

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

Step 3

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

$10 (\log (a) - (- 16 \cdot 1)) - 10 \log (\frac{V}{10^{- 16}})$

Step 4

Multiply $- 16$ by $1$ .

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

Step 5

Multiply $- 1$ by $- 16$ .

$10 (\log (a) + 16) - 10 \log (\frac{V}{10^{- 16}})$

Step 6

Rewrite $\log (\frac{V}{10^{- 16}})$ as $\log (V) - \log (10^{- 16})$ .

$10 (\log (a) + 16) - 10 (\log (V) - \log (10^{- 16}))$

Step 7

Expand $\log (10^{- 16})$ by moving $- 16$ outside the logarithm.

$10 (\log (a) + 16) - 10 (\log (V) - (- 16 \log (10)))$

Step 8

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

$10 (\log (a) + 16) - 10 (\log (V) - (- 16 \cdot 1))$

Step 9

Multiply $- 16$ by $1$ .

$10 (\log (a) + 16) - 10 (\log (V) - - 16)$

Step 10

Multiply $- 1$ by $- 16$ .

$10 (\log (a) + 16) - 10 (\log (V) + 16)$

Step 11

Simplify each term.

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Step 11.1

Apply the distributive property.

$10 \log (a) + 10 \cdot 16 - 10 (\log (V) + 16)$

Step 11.2

Multiply $10$ by $16$ .

$10 \log (a) + 160 - 10 (\log (V) + 16)$

Step 11.3

Apply the distributive property.

$10 \log (a) + 160 - 10 \log (V) - 10 \cdot 16$

Step 11.4

Multiply $- 10$ by $16$ .

$10 \log (a) + 160 - 10 \log (V) - 160$

Step 12

Subtract $160$ from $160$ .

$10 \log (a) + 0 - 10 \log (V)$

Step 13

Add $10 \log (a)$ and $0$ .

$10 \log (a) - 10 \log (V)$