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`

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

(1/3)^-a=81

=> (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.**

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.