Calculus Examples

$\log (2) \cdot 12 - \log (2) \cdot 3^{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply $\log (2) \cdot 12$ .

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Step 1.1.1

Reorder $\log (2)$ and $12$ .

$12 \cdot \log (2) - \log (2) \cdot 3^{2}$

Step 1.1.2

Simplify $12 \cdot \log (2)$ by moving $12$ inside the logarithm.

$\log (2^{12}) - \log (2) \cdot 3^{2}$

Step 1.2

Raise $2$ to the power of $12$ .

$\log (4096) - \log (2) \cdot 3^{2}$

Step 1.3

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

$\log (4096) - \log (2) \cdot 9$

Step 1.4

Multiply $- \log (2) \cdot 9$ .

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Step 1.4.1

Multiply $9$ by $- 1$ .

$\log (4096) - 9 \log (2)$

Step 1.4.2

Simplify $- 9 \log (2)$ by moving $9$ inside the logarithm.

$\log (4096) - \log (2^{9})$

Step 1.5

Raise $2$ to the power of $9$ .

$\log (4096) - \log (512)$

Step 2

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

$\log (\frac{4096}{512})$

Step 3

Divide $4096$ by $512$ .

$\log (8)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (8)$

Decimal Form:

$0.90308998 \dots$