Algebra Examples

$\ln (e^{4}) + \ln (e^{- 7})$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\ln (e^{4} e^{- 7})$

Step 2

Multiply $e^{4}$ by $e^{- 7}$ by adding the exponents.

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Step 2.1

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

$\ln (e^{4 - 7})$

Step 2.2

Subtract $7$ from $4$ .

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

Step 3

Use logarithm rules to move $- 3$ out of the exponent.

$- 3 \ln (e)$

Step 4

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

$- 3 \cdot 1$

Step 5

Multiply $- 3$ by $1$ .

$- 3$