Prove that log(a) b = 1/(log(b) a)

Expert Answers

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

We have to prove that `log_a b = 1/(log_b a)`

Use the property for changing the base of logarithms: `log_a b = (log_c b)/(log_c a)`

Change the base of `log_a b` to b

`log_a b = (log_b b)/(log_b a)`

Use the property: `log_b b = 1`

=> `1/(log_b a)`

This proves that `log_a b = 1/(log_b a)`

Approved by eNotes Editorial Team
Illustration of a paper plane soaring out of a book

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