Precalculus Examples

$2 \ln (e^{A}) + 3 \ln (B^{e})$

Step 1

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

$2 (A \ln (e)) + 3 \ln (B^{e})$

Step 2

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

$2 (A \cdot 1) + 3 \ln (B^{e})$

Step 3

Multiply $A$ by $1$ .

$2 A + 3 \ln (B^{e})$

Step 4

Simplify $3 \ln (B^{e})$ by moving $3$ inside the logarithm.

$2 A + \ln ({(B^{e})}^{3})$

Step 5

Multiply the exponents in ${(B^{e})}^{3}$ .

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Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 A + \ln (B^{e \cdot 3})$

Step 5.2

Move $3$ to the left of $e$ .

$2 A + \ln (B^{3 e})$