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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

`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)

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial