What is ln(10xe^{(-x)/(50)}) ?

The solution to ln(10xe^{(-x)/(50)}) is ln(10)+ln(x)-x/(50)

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simplify ln(10xe^{(-x)/(50)})

simplify

ln (10 x e^{\frac{- x}{50}})

ln (10) + ln (x) - \frac{x}{50}

Solution steps

ln (10 x e^{\frac{- x}{50}})

Apply log rule:

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

ln (10 x e^{\frac{- x}{50}}) = ln (10) + ln (x) + ln (e^{\frac{- x}{50}})

= ln (10) + ln (x) + 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 (10) + ln (x) + \frac{- x}{50} ln (e)

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

= ln (10) + ln (x) - \frac{x}{50}

lo g_{10} (\frac{3 x ^{2} - 15 x}{x ^{2} + 4 x})

ln (\frac{12 x ^{5}}{y})

50 \cdot ln (\frac{54.8}{29.5})

ln (\frac{1}{x}) - ln (\frac{2}{x})

- lo g_{10} (2.8 \cdot 1 0^{- 9})

What is ln(10xe^{(-x)/(50)}) ?
The solution to ln(10xe^{(-x)/(50)}) is ln(10)+ln(x)-x/(50)