Precalculus Examples

$3 \cdot \log_{9} (10) - 2 \cdot \log_{9} (5)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log_{9} (10)$ by moving $3$ inside the logarithm.

$\log_{9} (10^{3}) - 2 \cdot \log_{9} (5)$

Step 1.2

Raise $10$ to the power of $3$ .

$\log_{9} (1000) - 2 \cdot \log_{9} (5)$

Step 1.3

Simplify $- 2 \log_{9} (5)$ by moving $2$ inside the logarithm.

$\log_{9} (1000) - \log_{9} (5^{2})$

Step 1.4

Raise $5$ to the power of $2$ .

$\log_{9} (1000) - \log_{9} (25)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{9} (\frac{1000}{25})$

Step 3

Divide $1000$ by $25$ .

$\log_{9} (40)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log_{9} (40)$

Decimal Form:

$1.67888139 \dots$