Question

If log_x 9 – log_x 3 – log_x 27 = 2, then x is equal to ______.

Options

• 9

• 3

• `1/9`

• `1/3`

Answer 1

If log_x 9 – log_x 3 – log_x 27 = 2, then x is equal to `underlinebb(1/3)`.

Explanation:

log_x 9 – log_x 3 – log_x 27

= `log_x (9/3) - log_x 27`

= log_x 3 – log_x 27 

= `log_x (3/27)`

= `log_x (1/9)`

So `log_x (1/9) = 2` which means `x^2 = 1/9`. 

Hence `x = ±1/3`. 

The base x must be positive and not 1.

So `x = 1/3`.