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

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

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`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

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