Evaluate natural log of e^3+ natural log of e^7

$\ln (e^{3}) + \ln (e^{7})$

Step 1

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

$\ln (e^{3} e^{7})$

Step 2

Multiply $e^{3}$ by $e^{7}$ by adding the exponents.

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

$\ln (e^{3 + 7})$

Add $3$ and $7$ .

$\ln (e^{10})$

Step 3

Use logarithm rules to move $10$ out of the exponent.

$10 \ln (e)$

Step 4

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

$10 \cdot 1$

Step 5

Multiply $10$ by $1$ .

$10$