What is ln((24e^{-x-y})^5)+ln((15e^{3x-y})^3) ?

The solution to ln((24e^{-x-y})^5)+ln((15e^{3x-y})^3) is ln(26873856000e^{4x-8y})

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simplify ln((24e^{-x-y})^5)+ln((15e^{3x-y})^3)

simplify

ln ((24 e^{- x - y})^{5}) + ln ((15 e^{3 x - y})^{3})

ln (26873856000 e^{4 x - 8 y})

Solution steps

ln ((24 e^{- x - y})^{5}) + ln ((15 e^{3 x - y})^{3})

Apply log rule:

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

ln ((24 e^{- x - y})^{5}) + ln ((15 e^{3 x - y})^{3}) = ln ((24 e^{- x - y})^{5} (15 e^{3 x - y})^{3})

= ln ((24 e^{- x - y})^{5} (15 e^{3 x - y})^{3})

Simplify

(24 e^{- x - y})^{5} (15 e^{3 x - y})^{3} : 26873856000 e^{4 x - 8 y}

= ln (26873856000 e^{4 x - 8 y})

ln (\frac{0.85}{0.6108})

lo g_{3} ((6 x)^{2})

lo g_{10} (\frac{y ^{4} x ^{2}}{z})

ln (2) - ln (4) - ln (1) + ln (3)

What is ln((24e^{-x-y})^5)+ln((15e^{3x-y})^3) ?
The solution to ln((24e^{-x-y})^5)+ln((15e^{3x-y})^3) is ln(26873856000e^{4x-8y})