Precalculus Examples

$\log (\frac{9}{10})$

Step 1

Rewrite $\frac{9}{10}$ as $9 \cdot 10^{- 1}$ .

$\log (9 \cdot 10^{- 1})$

Step 2

Rewrite $\log (9 \cdot 10^{- 1})$ as $\log (9) + \log (10^{- 1})$ .

$\log (9) + \log (10^{- 1})$

Step 3

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

$\log (9) - \log (10)$

Step 4

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

$\log (9) - 1 \cdot 1$

Step 5

Multiply $- 1$ by $1$ .

$\log (9) - 1$

Step 6

Simplify each term.

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Step 6.1

Rewrite $\log (9)$ as $\log (3^{2})$ .

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

Step 6.2

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

$2 \log (3) - 1$

Step 7

Simplify each term.

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Step 7.1

Simplify $2 \log (3)$ by moving $2$ inside the logarithm.

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

Step 7.2

Raise $3$ to the power of $2$ .

$\log (9) - 1$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\log (9) - 1$

Decimal Form:

$- 0.04575749 \dots$