Precalculus Examples

$\ln ({(4)}^{2}) - 4 \ln (4)$

Step 1

Simplify each term.

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Step 1.1

Raise $4$ to the power of $2$ .

$\ln (16) - 4 \ln (4)$

Step 1.2

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

$\ln (16) - \ln (4^{4})$

Step 1.3

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

$\ln (16) - \ln (256)$

Step 2

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

$\ln (\frac{16}{256})$

Step 3

Cancel the common factor of $16$ and $256$ .

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Step 3.1

Factor $16$ out of $16$ .

$\ln (\frac{16 (1)}{256})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $16$ out of $256$ .

$\ln (\frac{16 \cdot 1}{16 \cdot 16})$

Step 3.2.2

Cancel the common factor.

$\ln (\frac{16 \cdot 1}{16 \cdot 16})$

Step 3.2.3

Rewrite the expression.

$\ln (\frac{1}{16})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\ln (\frac{1}{16})$

Decimal Form:

$- 2.77258872 \dots$