Question

Find the value of x if `5^(x - 1) + 5^x + 5^(x + 1) = 775`

Answer 1

We need to solve:

`5^(x - 1) + 5^x + 5^(x + 1) = 775`

Step 1: Factorize

Notice all terms involve powers of 5.

Factor out `5^(x - 1)`:

`5^(x - 1)(1 + 5 + 25) = 775`

`5^(x - 1)(31) = 775`

Step 2: Simplify

`5^(x - 1) = 775/31`

`5^(x - 1) = 25`

Step 3: Express as a power of 5

25 = 5²

So, `5^(x - 1) = 5^2`

⇒ x – 1 = 2

⇒ x = 2 + 1

⇒ x = 3