Solve:

Question

(1/81)^t=243^t-2

The book states to get the same base but I don't understand.

Thanks for any help.

Answer 1

the key is to recognize
both 81 and 243 as powers of 3

81 = 3^4 and 243 = 3^5

so (1/81)^t=243^t-2
(3^-4)^t = (3^5)^(t-2)

3^(-4t) = 3^(5t-10)

then -4t = 5t - 10
-9t=-10
t=10/9