Precalculus Examples

$4 \ln (\frac{3 (e^{3})}{3}) = 12$

Step 1

Simplify $4 \log_{2.71828182} (\frac{3 {(2.71828182)}^{3}}{3})$ .

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

Cancel the common factor.

$4 \log_{2.71828182} (\frac{3 {(2.71828182)}^{3}}{3}) = 12$

Step 1.1.2

Divide ${(2.71828182)}^{3}$ by $1$ .

$4 \log_{2.71828182} ({(2.71828182)}^{3}) = 12$

Step 1.2

Use logarithm rules to move $3$ out of the exponent.

$4 (3 \log_{2.71828182} (2.71828182)) = 12$

Step 1.3

Log base $2.71828182$ of $2.71828182$ is approximately $1$ .

$4 (3 \cdot 1) = 12$

Step 1.4

Multiply $3$ by $1$ .

$4 \cdot 3 = 12$

Step 1.5

Multiply $4$ by $3$ .

$12 = 12$

Step 2

Since $12 = 12$ , the equation will always be true.

Always true

Step 3

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$