Calculus Examples

$12 \log_{9} (12) - 3 \log_{9} (5)$

Step 1

Simplify each term.

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Step 1.1

Simplify $12 \log_{9} (12)$ by moving $12$ inside the logarithm.

$\log_{9} (12^{12}) - 3 \log_{9} (5)$

Step 1.2

Raise $12$ to the power of $12$ .

$\log_{9} (8916100448256) - 3 \log_{9} (5)$

Step 1.3

Simplify $- 3 \log_{9} (5)$ by moving $3$ inside the logarithm.

$\log_{9} (8916100448256) - \log_{9} (5^{3})$

Step 1.4

Raise $5$ to the power of $3$ .

$\log_{9} (8916100448256) - \log_{9} (125)$

Step 2

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

$\log_{9} (\frac{8916100448256}{125})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\log_{9} (\frac{8916100448256}{125})$

Decimal Form:

$11.37369676 \dots$