What is ln((sqrt(5))/(4m^8)) ?

The solution to ln((sqrt(5))/(4m^8)) is 1/2 ln(5)-2ln(2)-8ln(m)

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simplify ln((sqrt(5))/(4m^8))

simplify

ln (\frac{5}{4 m ^{8}})

\frac{1}{2} ln (5) - 2 ln (2) - 8 ln (m)

Solution steps

ln (\frac{5}{4 m ^{8}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{5}{4 m ^{8}}) = ln (5) - ln (4 m^{8})

= ln (5) - ln (4 m^{8})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (4 m^{8}) = ln (4) + ln (m^{8})

= ln (5) - (ln (m^{8}) + ln (4))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (m^{8}) = 8 ln (m)

= ln (5) - (ln (4) + 8 ln (m))

ln (5) = \frac{1}{2} ln (5)

- (ln (4) + 8 ln (m)) = - (2 ln (2) + 8 ln (m))

= \frac{1}{2} ln (5) - (8 ln (m) + 2 ln (2))

- (2 ln (2) + 8 ln (m)) : - 2 ln (2) - 8 ln (m)

= \frac{1}{2} ln (5) - 2 ln (2) - 8 ln (m)

ln (\frac{54000}{50000})

ln (w x yz)

ln (\frac{- 1}{x ^{2}} e^{x})

lo g_{10} ((1 - i)^{4})

2 + 2 lo g_{2} (π) - lo g_{2} (30)

What is ln((sqrt(5))/(4m^8)) ?
The solution to ln((sqrt(5))/(4m^8)) is 1/2 ln(5)-2ln(2)-8ln(m)