Precalculus Examples

$\ln (\frac{x}{e}) x$

Step 1

Rewrite $\frac{x}{e}$ as $x e^{- 1}$ .

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

Step 2

Rewrite $\ln (x e^{- 1})$ as $\ln (x) + \ln (e^{- 1})$ .

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

Step 3

Use logarithm rules to move $- 1$ out of the exponent.

$(\ln (x) - \ln (e)) x$

Step 4

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

$(\ln (x) - 1 \cdot 1) x$

Step 5

Multiply $- 1$ by $1$ .

$(\ln (x) - 1) x$

Step 6

Apply the distributive property.

$\ln (x) x - 1 x$

Step 7

Simplify the expression.

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Step 7.1

Rewrite $- 1 x$ as $- x$ .

$\ln (x) x - x$

Step 7.2

Reorder factors in $\ln (x) x - x$ .

$x \ln (x) - x$

Step 7.3

Reorder $x \ln (x)$ and $- x$ .

$- x + x \ln (x)$