Question #64391

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Answer 1 · 2017-09-17T22:40:50

#t = ln(frac(13)(25))#

We have: #25 (1 - e^(t)) = 12#

Divide both sides of the equation by #25#:

#Rightarrow 1 - e^(t) = frac(12)(25)#

Subtract #1# from both sides:

#Rightarrow - e^(t) = - frac(13)(25)#

Multiply both sides by #- 1#:

#Rightarrow e^(t) = frac(13)(25)#

Apply #ln# to both sides:

#Rightarrow ln(e^(t)) = ln(frac(13)(25))#

Using the laws of logarithms:

#Rightarrow t ln(e) = ln(frac(13)(25))#

#Rightarrow t cdot 1 = ln(frac(13)(25))#

#therefore t = ln(frac(13)(25))#

Therefore, the solution to the equation is #ln(frac(13)(25))#.