How do you move e^x to the other side the equation?

Question

I guess my instructor left out this basic algebra here...So I have the following:

8e^9t = 11e^8t

I want to know how to get one of those e^"t"s to the other side so I can solve for T. thanks.

Answer 1

8e^9t = 11e^8t

Divide each side by e^8t.

8e^t = 11

Divide each side by 8.

e^t = 11/8.

Apply 'log' each side.

log(e^t) = log(11/8).

Natural logarithm formula and table log aⁿ = n log a, log e = 1 and log(11/8) ≈ 0.31845

t log(e) = 0.31845.

t(1) = 0.31845.

t = 0.31845.