Question

Evaluate the following by converting into exponential form:

`log_(sqrt(3)) 9`

Answer 1

Given: `log_(sqrt(3)) 9`

Step-wise calculation:

Let `log_(sqrt(3)) 9 = x`. 

Then `(sqrt(3))^x = 9`. 

Write `sqrt(3) = 3^(1/2)`, 

So `(3^(1/2))^x = 3^(x/2)` 

`(3^(1/2))^x = 3^2` 

Equate exponents:

`x/2 = 2` 

⇒ x = 4 

This follows the same conversion method shown in the provided examples.

`log_(sqrt(3)) 9 = 4`