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

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

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Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
4.9 4.9 (174 lesson ratings) (174)
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(1/5)x=√5 or
Clearly, -x=½ or x=-½
Here I used the fact that (a/b)n=an/bn; 1/an=a-n; for any n.


This one is easier to understand - you don't have to go into logarithm.
Thank you so much for explaining it in a way I can understand. I really appreciate it.
Jessica G. | Experienced SAT Prep and Math tutorExperienced SAT Prep and Math tutor
4.9 4.9 (110 lesson ratings) (110)
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!