Precalculus Examples

$\frac{2 \ln (7 - 3)}{3 {(7)}^{3}}$

Step 1

Simplify $2 \ln (7 - 3)$ by moving $2$ inside the logarithm.

$\frac{\ln ({(7 - 3)}^{2})}{3 \cdot 7^{3}}$

Step 2

Raise $7$ to the power of $3$ .

$\frac{\ln ({(7 - 3)}^{2})}{3 \cdot 343}$

Step 3

Simplify the numerator.

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Step 3.1

Subtract $3$ from $7$ .

$\frac{\ln (4^{2})}{3 \cdot 343}$

Step 3.2

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

$\frac{\ln (16)}{3 \cdot 343}$

Step 4

Multiply $3$ by $343$ .

$\frac{\ln (16)}{1029}$

Step 5

Rewrite $\frac{\ln (16)}{1029}$ as $\frac{1}{1029} \ln (16)$ .

$\frac{1}{1029} \ln (16)$

Step 6

Simplify $\frac{1}{1029} \ln (16)$ by moving $\frac{1}{1029}$ inside the logarithm.

$\ln (16^{\frac{1}{1029}})$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\ln (16^{\frac{1}{1029}})$

Decimal Form:

$0.00269444 \dots$