^{x}=√5 or

^{-x}=5

^{½}

^{n}=a

^{n}/b

^{n}; 1/a

^{n}=a

^{-n}; for any n.

^{ }

Answers given

{-1/2}

{-1}

{-2}

{-3/2}

I only have two more weeks and I am brain dead here

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Marked as Best Answer

(1/5)^{x}=√5 or

5^{-x}=5^{½}

Clearly, -x=½ or x=-½

Here I used the fact that (a/b)^{n}=a^{n}/b^{n}; 1/a^{n}=a^{-n}; for any n.^{
}

Jessica G. | Experienced SAT Prep and Math tutorExperienced SAT Prep and Math tutor

Hi Debra,

This problem requires the use of a logarithm. Using the transitive property, we know that if g(x) is equal to both (1/5)^x and sqrt(5) then (1/5)^x = sqrt(5). A logarithm helps us "undo" an equation where the variable is in the exponent. Specifically, if a^b=c, we have log{base a}(c)=b. In your case, we would have log{base 1/5}(sqrt(5))=x. If you have a calculator, simply plug this guy in and you're golden. I'm sure google could do it for you as well!

Cheers,

Jess

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