What is ln((m^3)/(b^2)) ?

The solution to ln((m^3)/(b^2)) is 3ln(m)-2ln(b)

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simplify ln((m^3)/(b^2))

simplify

ln (\frac{m ^{3}}{b ^{2}})

3 ln (m) - 2 ln (b)

Solution steps

ln (\frac{m ^{3}}{b ^{2}})

Apply log rule:

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

ln (\frac{m ^{3}}{b ^{2}}) = ln (m^{3}) - ln (b^{2})

= ln (m^{3}) - ln (b^{2})

Apply log rule:

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

ln (m^{3}) = 3 ln (m)

= 3 ln (m) - ln (b^{2})

Apply log rule:

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

ln (b^{2}) = 2 ln (b)

= 3 ln (m) - 2 ln (b)

ln (\frac{1}{125}) + 4 ln (5) - 2 ln (\frac{1}{5})

ln (\frac{1}{x}) - ln (x)

\frac{6}{5} ln \frac{y}{x} - 1 - \frac{1}{5} ln \frac{y}{x} + 4 + ln ∣ x ∣

0.77 + \frac{8.134 \cdot 298}{1 \cdot 96500} \cdot ln (\frac{1}{4})

ln (\frac{1}{2} e)