SOLUTION: How to use exponential to solve the following equation (i) 4e(to the power 3t+5) = 4/e(to the power t)

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Question 502982: How to use exponential to solve the following equation (i) 4e(to the power 3t+5) = 4/e(to the power t)
Answer by jrb1965(16) About Me  (Show Source):
You can put this solution on YOUR website!
You want to solve the following equation for t
4e%5E%283t%2B5%29 = 4%2F%28e%5Et%29
Remember when you multiply, you add exponents, so multiply both sides of the equation by e%5Et, and then divide by 4
4%28e%5E%283t%2B5%29%29e%5Et = 4
e%5E%284t%2B5%29 = 1
To simplify an exponential function take the logarithm (ln) of both sides
ln%28e%5E%284t%2B5%29%29 = ln(1) = 0
By definition ln%28e%5E%28x%29%29 = x, and ln(1) = 0, so
4t + 5 = 0
4t = -5
t = -5/4 = - 1.25