Question

Solve 2^t-2^t-1=40

Answer 1

the way you typed it,

2^t-2^t-1=40
you would get:
0 - 1 = 40, which of course is a false statement

you must have meant:
2^t-2^(t-1)=40
take out a factor of 2^(t-1)
2^(t-1) [2 - 1] = 40
2^(t-1) = 39
take logs of both sides, and use log rules
(t-1)log2 = log39
t-1 = log39/log2 = appr 5.2854

t = 6.2854