Algebra: Solve for t: e (exponent: 2t-5) = 5000?

Question

It says to find two answers:
A. exact answer
B. approx. answer (round to 3 decimal places)

Any help would be greatly appreciated!

Answer 1

Hello Deepblue,

take the ln of both sides giving us

ln e^(2t-5) = ln5000

Now the ln of a power is the power times the ln so :

(2t-5)ln e = ln5000, but ln e = 1 hence:

2t-5 = ln 5000

solving for gives us:

t = (ln 5000 + 5)/2 Exact answer.

Answer rounded to nearest three places = (8.51719 +5)/2 =

6.76.

Hope This Helps!!

Answer 2

e^(2t - 5) = 5000
2t - 5 = ln(5000)
2t = 5 + ln(5000)
t = (5 + ln(5000))/2

about 6.759

Answer 3

e^(2t - 5) = 5000

ln e^ (2t - 5) = ln 5000

2t - 5 = ln 5000

2t = 5 + ln 5000

t = 2.5 + 0.5 ln 5000

t = 6.759