Precalculus Examples

$- \log (1.3 x \cdot 10^{- 4})$

Step 1

Rewrite $\log (1.3 x \cdot 10^{- 4})$ as $\log (1.3 x) + \log (10^{- 4})$ .

$- (\log (1.3 x) + \log (10^{- 4}))$

Step 2

Rewrite $\log (1.3 x)$ as $\log (1.3) + \log (x)$ .

$- (\log (1.3) + \log (x) + \log (10^{- 4}))$

Step 3

Expand $\log (10^{- 4})$ by moving $- 4$ outside the logarithm.

$- (\log (1.3) + \log (x) - 4 \log (10))$

Step 4

Log base $10$ of $1.3$ is approximately $0.11394335$ .

$- (0.11394335 + \log (x) - 4 \log (10))$

Step 5

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

$- (0.11394335 + \log (x) - 4 \cdot 1)$

Step 6

Multiply $- 4$ by $1$ .

$- (0.11394335 + \log (x) - 4)$

Step 7

Subtract $4$ from $0.11394335$ .

$- (- 3.88605664 + \log (x))$

Step 8

Apply the distributive property.

$- - 3.88605664 - \log (x)$

Step 9

Multiply $- 1$ by $- 3.88605664$ .

$3.88605664 - \log (x)$