Question

3. If log 2 =a and log 3=b, the expression 9/32
is equivalent to

Answer 1

`(9)/(32) = \frac{{10}^(2b) }{{10}^(5a)}`

Explanation:

It is given that:

log 2=a and log 3=b

This implies that:

`2 = {10}^(a)`

and

`3 = {10}^(b)`

Now we know that:

`(9)/(32) = \frac{ {3}^(2) }{ {2}^(5) }`

We substitute to get:

`(9)/(32) = \frac{ ({10}^(b)) ^(2) }{( {10}^(a))^(5) }`

We simplify to get:

`(9)/(32) = \frac{{10}^(2b) }{{10}^(5a)}`