Solve the following for x, 5^(1-x) =25

Answer 1

There are 2 ways to solve it. Stephanie's is the simpler way, which can be used for this example.

Another method you can use is to use log() on both sides (or ln() ):

If you ln both sides, then (1 - x) can be brought down

ln [5^{(1 - x)}] = ln [25]

(1 - x)* ln[5] = ln [25]

divide both sides by ln[5]:

(1 - x) = ln[25] / ln[5]:

1 - x = 2

-x = 2 -1 = 1

x = -1

Answer 2

5^(1-x) =25, we write the right sides as base 5

5^(1-x) =5²

Now since the base on both sides is the same, we can compare the exponents

1-x =2

x = 1 - 2 = -1