let g(x) = (1/5)^x. Solve g(x) = sqrt(5)

Question

Answers given 

{-1/2}

{-1}

{-2}

{-3/2}

 

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

 

Answer 1

(1/5)^x=√5 or

5^-x=5^½

Clearly, -x=½ or x=-½

 

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

Answer 2

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