Precalculus Examples

$t \ln (e^{\frac{t}{2}})$

Step 1

Expand $\ln (e^{\frac{t}{2}})$ by moving $\frac{t}{2}$ outside the logarithm.

$t (\frac{t}{2} \ln (e))$

Step 2

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

$t (\frac{t}{2} \cdot 1)$

Step 3

Multiply $\frac{t}{2}$ by $1$ .

$t \frac{t}{2}$

Step 4

Multiply $t \frac{t}{2}$ .

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Step 4.1

Combine $t$ and $\frac{t}{2}$ .

$\frac{t \cdot t}{2}$

Step 4.2

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

$\frac{t^{1} t}{2}$

Step 4.3

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

$\frac{t^{1} t^{1}}{2}$

Step 4.4

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

$\frac{t^{1 + 1}}{2}$

Step 4.5

Add $1$ and $1$ .

$\frac{t^{2}}{2}$