What is ln(((c^{1-n}m^n)^{1-l})/(1-l)) ?

The solution to ln(((c^{1-n}m^n)^{1-l})/(1-l)) is (1-l)ln(c^{1-n}m^n)-ln(1-l)

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simplify ln(((c^{1-n}m^n)^{1-l})/(1-l))

simplify

ln (\frac{( c ^{1 - n} m ^{n} ) ^{1 - l}}{1 - l})

(1 - l) ln (c^{1 - n} m^{n}) - ln (1 - l)

Solution steps

ln (\frac{( c ^{1 - n} m ^{n} ) ^{1 - l}}{1 - l})

Apply log rule:

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

ln (\frac{( c ^{1 - n} m ^{n} ) ^{1 - l}}{1 - l}) = ln ((c^{1 - n} m^{n})^{1 - l}) - ln (1 - l)

= ln ((c^{- n + 1} m^{n})^{- l + 1}) - ln (- l + 1)

Apply log rule:

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

ln ((c^{1 - n} m^{n})^{1 - l}) = (1 - l) ln (c^{1 - n} m^{n})

= (1 - l) ln (c^{1 - n} m^{n}) - ln (1 - l)

20 lo g_{10} (2) + 40 lo g_{10} (0.04)

lo g_{3} (\frac{1}{16}) - 1

lo g_{10} (\frac{x}{2})

ln (\frac{x ^{3}}{x ( 1 + x ) ^{2}})

What is ln(((c^{1-n}m^n)^{1-l})/(1-l)) ?
The solution to ln(((c^{1-n}m^n)^{1-l})/(1-l)) is (1-l)ln(c^{1-n}m^n)-ln(1-l)