Precalculus Examples

$\log (40) + \log (\frac{1}{10})$

Step 1

Rewrite $\log (\frac{1}{10})$ as $\log (1) - \log (10)$ .

$\log (40) + \log (1) - \log (10)$

Step 2

Logarithm base $10$ of $1$ is $0$ .

$\log (40) + 0 - \log (10)$

Step 3

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

$\log (40) + 0 - 1 \cdot 1$

Step 4

Multiply $- 1$ by $1$ .

$\log (40) + 0 - 1$

Step 5

Subtract $1$ from $0$ .

$\log (40) - 1$

Step 6

Simplify each term.

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Step 6.1

Rewrite $\log (40)$ as $\log (2^{3} \cdot 5)$ .

$\log (2^{3} \cdot 5) - 1$

Step 6.2

Rewrite $\log (2^{3} \cdot 5)$ as $\log (2^{3}) + \log (5)$ .

$\log (2^{3}) + \log (5) - 1$

Step 6.3

Expand $\log (2^{3})$ by moving $3$ outside the logarithm.

$3 \log (2) + \log (5) - 1$