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

Question

asked Dec 15, 2021 86.1k views

1 Answer

Ptkato · Answer 1 · 2021-12-20T17:43:02+0000

Answer:

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

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:

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