SOLUTION: Can you please help me evaluate 5^log1/5(1/2) Thank in advance Vijji

Question 638062: Can you please help me evaluate 5^log1/5(1/2)
Thank in advance
Vijji
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it's hard to determine what your problem is.
this is what i think it is.
5^(log(1/5,(1/2)
what this means is 5 raised to the power of (the log of 1/2 to the base of 1/5).
if that's what you meant, then the solution would be as follows.
let 1/2 = .5
let 1/5 = .2
problem then becomes:
5^(log of .5 to the base of .2)
first think we want to do is convert the log from the base of .2 to the base of 10.
this allows you to use the LOG function of your calculator.
the conversion formula would be:
log of .5 to the base of .2 equals the log of .5 to the base of 10 divided by the log of .2 to the base of 10.
the log of .5 to the base of 10 divided by the log of .2 to the base of 10 would look like:
LOG(.5)/LOG(.2)
replacing that in your expression make your expression equal to:
5^(LOG(.5)/LOG(.2))
use your calculator to solve for LOG(.5)/LOG(.2) and your expression becomes:
5^(.4306765581)
use your calculator again to get:
5^(.4306765581) = 2.
that's your answer assuming i interpreted your problem correctly.

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