How do you evaluate $ln (\frac{1}{{\sqrt{e}}^{7}})$ $ln(1/sqrt e^7)$ ?

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How do you evaluate $ln (\frac{1}{{\sqrt{e}}^{7}})$ $ln(1/sqrt e^7)$ ?

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Answer 1 · 2016-03-22T16:34:42

$ln (\frac{1}{{\sqrt{e}}^{7}}) = - \frac{7}{2}$ $ln(1/sqrte ^7) = -7/2$

Explanation:

$ln (\frac{1}{{\sqrt{e}}^{7}})$ $ln(1/sqrte ^7)$
$= ln 1 - {ln \sqrt{e}}^{7}$ $=ln 1 - lnsqrte^7$ -> use property ${log}_{b} (\frac{x}{y}) = {log}_{b} x - {log}_{b} y$ $log_b(x/y)=log_bx-log_by$
$= 0 - {ln e}^{\frac{7}{2}}$ $=0-lne^(7/2)$ -> $ln 1 = 0$ $ln 1=0$
$= - \frac{7}{2} ln e$ $=-7/2 ln e$ ->use property ${log}_{b} x^{n} = n \cdot {log}_{b} x$ $log_b x^n=n*log_bx$
$= - \frac{7}{2} \cdot 1$ $=-7/2 * 1$ -> $ln e = 1$ $ln e =1$
$= - \frac{7}{2}$ $=-7/2$

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How do you evaluate $ln (\frac{1}{{\sqrt{e}}^{7}})$ $ln(1/sqrt e^7)$ ?

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