Precalculus Examples

$\ln ({(54.598)}^{2}) - 3 \ln (54.598 - 4)$

Step 1

Simplify each term.

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Step 1.1

Raise $54.598$ to the power of $2$ .

$\ln (2980.941604) - 3 \ln (54.598 - 4)$

Step 1.2

Subtract $4$ from $54.598$ .

$\ln (2980.941604) - 3 \ln (50.598)$

Step 1.3

Simplify $- 3 \ln (50.598)$ by moving $3$ inside the logarithm.

$\ln (2980.941604) - \ln ({50.598}^{3})$

Step 1.4

Raise $50.598$ to the power of $3$ .

$\ln (2980.941604) - \ln (129538.85444719)$

Step 2

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

$\ln (\frac{2980.941604}{129538.85444719})$

Step 3

Divide $2980.941604$ by $129538.85444719$ .

$\ln (0.02301194)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\ln (0.02301194)$

Decimal Form:

$- 3.77174164 \dots$