Algebra Examples

$0.5 e^{2 \ln (x)} + 2 \ln (e^{x})$

Step 1

Simplify $2 \ln (x)$ by moving $2$ inside the logarithm.

$0.5 e^{\ln (x^{2})} + 2 \ln (e^{x})$

Step 2

Exponentiation and log are inverse functions.

$0.5 x^{2} + 2 \ln (e^{x})$

Step 3

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

$0.5 x^{2} + 2 (x \ln (e))$

Step 4

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

$0.5 x^{2} + 2 (x \cdot 1)$

Step 5

Multiply $x$ by $1$ .

$0.5 x^{2} + 2 x$