Change the exponential expression (1/3)^-a=81 to an equivalent expression involving a logarithm.

Expert Answers

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

To convert an exponential equation to a logarithmic equation note that `log_b c=x <=> b^x=c` .

So for this equation we get `log_(1/3)81=-a`

Alternatively, you could rewrite the original equation as `(3^(-1))^(-a)=81` or `3^a=81` , and so write as a logaritmic equation as `log_3 81 = a` .

In either case, the solution is a=4 since `81=3^4`

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

The exponential expression (1/3)^-a=81 needs to be converted to an expression involving a logarithm.


=> (1/3)^-a = 3^4

take the log of both the sides

log((1/3)^-a) = log(3^4)

use the property of logarithms: log x^a = a*log x

=> -a*log(1/3) = 4* log 3

=> -a*log(3^-1) = 4*log 3

=> -1*-a*log 3 = 4*log 3

=> a*log 3 = 4*log 3

=> a = 4

The given expression is simplified to the form a = 4.

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