How do you change ${(\frac{1}{5})}^{4} = \frac{1}{625}$ $(1/5)^4 = 1/625$ into log form?

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How do you change ${(\frac{1}{5})}^{4} = \frac{1}{625}$ $(1/5)^4 = 1/625$ into log form?

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Answer 1 · 2016-07-15T17:09:35

$4 ln (5) = ln (625)$ $4ln(5) = ln(625)$

Explanation:

if by log form you are referring to the natural logarithm then you apply the function as such

$ln ({(\frac{1}{5})}^{4}) = ln (\frac{1}{625})$ $ln((1/5)^4) = ln(1/625)$

$4 ln (\frac{1}{5}) = ln (\frac{1}{625})$ $4ln(1/5) = ln(1/625)$

$4 ln (1) - 4 ln (5) = ln (1) - ln (625)$ $4ln(1) - 4ln(5) = ln(1) -ln(625)$
technically the log of anything that is 1 is 0
$- 4 ln (5) = - ln (625)$ $- 4ln(5) = -ln(625)$
$4 ln (5) = ln (625)$ $4ln(5) = ln(625)$

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How do you change ${(\frac{1}{5})}^{4} = \frac{1}{625}$ $(1/5)^4 = 1/625$ into log form?

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How do you change ${(\frac{1}{5})}^{4} = \frac{1}{625}$ $(1/5)^4 = 1/625$ into log form?