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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)...

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christiano-cr7 | Salutatorian

Posted September 23, 2013 at 10:30 AM via web

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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

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 23, 2013 at 10:35 AM (Answer #1)

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`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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