Question

Find the value of x, if `5^(x - 3) xx 5^(2x – 8)` = 625.

Answer 1

Given: `5^(x - 3) xx 5^(2x – 8)` = 625.

⇒ `5^(x - 3) xx 5^(2x – 8)` = 5⁴

We know that if the basis is the same, then powers will be added.

∴ `5^((x - 3) + (2x – 8))` = 5⁴

`5^(3x - 11)` = 5⁴

We get by equating the exponents

3x – 11 = 4

⇒ 3x = 4 + 11

⇒ 3x = 15

⇒ x = 5

As a result, the value of x is 5.