What is ln(500e^{(-x)/(50)}) ?

The solution to ln(500e^{(-x)/(50)}) is ln(500)-x/(50)

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simplify ln(500e^{(-x)/(50)})

simplify

ln (500 e^{\frac{- x}{50}})

ln (500) - \frac{x}{50}

Solution steps

ln (500 e^{\frac{- x}{50}})

Apply log rule:

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

ln (500 e^{\frac{- x}{50}}) = ln (500) + ln (e^{\frac{- x}{50}})

= ln (500) + ln (e^{\frac{- x}{50}})

Apply log rule:

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

ln (e^{\frac{- x}{50}}) = \frac{- x}{50} ln (e)

= ln (500) + \frac{- x}{50} ln (e)

\frac{- x}{50} ln (e) = - \frac{x}{50}

= ln (500) - \frac{x}{50}

0 - \frac{0.025693}{2} ln (\frac{1}{2})

ln (e^{0} + 1) - ln (e^{- l n (2)} + 1)

ln (\frac{π}{x})

2 ln (5) + 2 ln (x) - 3

2 ln (3 x) + 5 ln (x - 7) - ln (x^{2} - 1)

What is ln(500e^{(-x)/(50)}) ?
The solution to ln(500e^{(-x)/(50)}) is ln(500)-x/(50)