What is ln(Ce^{-(3t)/(125)}) ?

The solution to ln(Ce^{-(3t)/(125)}) is ln(C)-(3t)/(125)

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simplify ln(Ce^{-(3t)/(125)})

simplify

ln (C e^{- \frac{3 t}{125}})

ln (C) - \frac{3 t}{125}

Solution steps

ln (C e^{- \frac{3 t}{125}})

Apply log rule:

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

ln (C e^{- \frac{3 t}{125}}) = ln (C) + ln (e^{- \frac{3 t}{125}})

= ln (C) + ln (e^{- \frac{3 t}{125}})

Apply log rule:

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

ln (e^{- \frac{3 t}{125}}) = - \frac{3 t}{125} ln (e)

= ln (C) - \frac{3 t}{125} ln (e)

\frac{3 t}{125} ln (e) = \frac{3 t}{125}

= ln (C) - \frac{3 t}{125}

ln (50) - ln (180)

- 1.25 ln (\frac{50}{100})

24 lo g_{2} (x) + 6 lo g_{2} (y)

ln (\frac{3}{14})

ln (x^{2}) - ln (y^{2}) - ln (3)

What is ln(Ce^{-(3t)/(125)}) ?
The solution to ln(Ce^{-(3t)/(125)}) is ln(C)-(3t)/(125)