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Popular >

simplify ln((m^3)/(n^7))

Solution

simplify

ln (\frac{m ^{3}}{n ^{7}})

Solution

3 ln (m) - 7 ln (n)

Solution steps

ln (\frac{m ^{3}}{n ^{7}})

Apply log rule:

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

ln (\frac{m ^{3}}{n ^{7}}) = ln (m^{3}) - ln (n^{7})

= ln (m^{3}) - ln (n^{7})

Apply log rule:

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

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

= 3 ln (m) - ln (n^{7})

Apply log rule:

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

ln (n^{7}) = 7 ln (n)

= 3 ln (m) - 7 ln (n)

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Frequently Asked Questions (FAQ)

What is ln((m^3)/(n^7)) ?
The solution to ln((m^3)/(n^7)) is 3ln(m)-7ln(n)