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