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 $ln(frac(13)(25))$ .