Do you need to solve for t?
Hint - take logs.
7^t-2 = 5^t
3 answers
yes
is it 7^(t-2) = 5^t or
7^t - 2 = 5^t ?
If it is the first way, then
log(7^(t-2)) = log 5^t
(t-2)log7 = tlog5
tlog7 - 2lo7 = tlog5
tlog7 - tlog5 = 2log7
t(log7 - log5) - 2log7
t = 2log7 / (log7 - log5)
t = 11.566542
for the second interpretation of your typing, one would have to use something like Newton's Method to solve it.
7^t - 2 = 5^t ?
If it is the first way, then
log(7^(t-2)) = log 5^t
(t-2)log7 = tlog5
tlog7 - 2lo7 = tlog5
tlog7 - tlog5 = 2log7
t(log7 - log5) - 2log7
t = 2log7 / (log7 - log5)
t = 11.566542
for the second interpretation of your typing, one would have to use something like Newton's Method to solve it.