Question

Find the value of x in the following:

`log_(sqrt(5))(x + 8) = 4`

Answer 1

To solve `log_(sqrt(5))(x + 8) = 4`, convert it to exponential form:

`(sqrt(5))^4 = x + 8`

Now calculate `(sqrt(5))^4`:

`(sqrt(5))^4 = (5^(1//2))^4`

= 5²

= 25

So x + 8 = 25

⇒ x = 25 – 8

⇒ x = 17