Precalculus Examples

$\ln (e^{- x^{2} \cdot (3 x)})$

Step 1

Use logarithm rules to move $- x^{2} \cdot (3 x)$ out of the exponent.

$- x^{2} \cdot (3 x) \ln (e)$

Step 2

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 2.1

Move $x$ .

$- (x \cdot x^{2}) \cdot 3 \ln (e)$

Step 2.2

Multiply $x$ by $x^{2}$ .

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Step 2.2.1

Raise $x$ to the power of $1$ .

$- (x^{1} x^{2}) \cdot 3 \ln (e)$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- x^{1 + 2} \cdot 3 \ln (e)$

Step 2.3

Add $1$ and $2$ .

$- x^{3} \cdot 3 \ln (e)$

Step 3

Multiply $3$ by $- 1$ .

$- 3 x^{3} \ln (e)$

Step 4

The natural logarithm of $e$ is $1$ .

$- 3 x^{3} \cdot 1$

Step 5

Multiply $- 3$ by $1$ .

$- 3 x^{3}$