How do you simplify ln ( 8 / e^7 )?

May 8, 2016

Answer:

$3 \ln 2 - 7 = - 4.92$, nearly.

Explanation:

Use $\ln \left(\frac{m}{n}\right) = \ln m - \ln n , \ln {a}^{n} = n \ln a \mathmr{and} \ln e = 1$

$\ln \left(\frac{8}{e} ^ 7\right) = \ln 8 - \ln \left({e}^{7}\right)$

$= \ln {2}^{3} - \ln {e}^{7}$

$= 3 \ln 2 - 7 \ln e = 3 \ln 2 - 7 \left(1\right)$