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

The solution to ln(24e^{-x-y})+ln(15e^{3x-y}) is ln(360e^{2x-2y})

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

simplify

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

ln (360 e^{2 x - 2 y})

Solution steps

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

Apply log rule:

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

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

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

Simplify

24 e^{- x - y} \cdot 15 e^{3 x - y} : 360 e^{2 x - 2 y}

= ln (360 e^{2 x - 2 y})

- ln (\frac{3.8}{16}) - ln (\frac{5}{16})

- lo g_{10} (4.51 \cdot 1 0^{- 6})

- lo g_{10} (2.3 \cdot 1 0^{- 4})

ln (\frac{75.5}{49.2})

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

What is ln(24e^{-x-y})+ln(15e^{3x-y}) ?
The solution to ln(24e^{-x-y})+ln(15e^{3x-y}) is ln(360e^{2x-2y})