Precalculus Examples

$\log (4) \cdot 192 - \log (4) \cdot 3$

Step 1

Simplify each term.

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Step 1.1

Multiply $\log (4) \cdot 192$ .

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Step 1.1.1

Reorder $\log (4)$ and $192$ .

$192 \cdot \log (4) - \log (4) \cdot 3$

Step 1.1.2

Simplify $192 \cdot \log (4)$ by moving $192$ inside the logarithm.

$\log (4^{192}) - \log (4) \cdot 3$

Step 1.2

Multiply $- \log (4) \cdot 3$ .

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Step 1.2.1

Multiply $3$ by $- 1$ .

$\log (4^{192}) - 3 \log (4)$

Step 1.2.2

Simplify $- 3 \log (4)$ by moving $3$ inside the logarithm.

$\log (4^{192}) - \log (4^{3})$

Step 1.3

Raise $4$ to the power of $3$ .

$\log (4^{192}) - \log (64)$

Step 2

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

$\log (\frac{4^{192}}{64})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{4^{192}}{64})$

Decimal Form:

$113.78933836 \dots$