Given that `log_b(a^2) = 3` , the value of `log_a(b^2)` is;

(a) 5/3

(b) 3/4

(c) 2/3

(d) 4/3

(e) 3/2

### 1 Answer | Add Yours

`log_b(a^2) = 3`

Remove the logarithm will give us;

`a^2 = b^3`

`b = (a^2)^(1/3)`

`b^2 = a^(4/3)`

Take log on both sides using a as base.

`log_a(b^2) = log_a(a^(4/3))`

`log_a(b^2) = 4/3log_a(a)`

`log_a(b^2) = 4/3`

*So the correct answer is at option d)*

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