SOLUTION: Solve for x: log(subscript5)(x)=-2. thanks.

Question 202239: Solve for x: log(subscript5)(x)=-2. thanks.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this says:

because logarithms are inverse of exponents, this formula can only be true if and only if...

which should be the same as:

since = 25, this becomes:
(1/25) = x
The answer should be (1/25)
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to prove this is true, substitute (1/25) for x and solve.

is the same as:

to solve using your calculator, you can convert the base 5 to the base 10 or to the natural log base.
let's try the base 10.
= 0/.698..... = 0
= 2
so...
which is true,
so x = (1/25) is a good answer.
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another way to prove it is to convert back to exponents by taking the inverse.
we start off with:

this is true if and only if:

we'll cheat this time by using the calculator.

.04 is the same as .04/1
multiply numerator and denominator by 25 (doesn't change the fraction), and we get
(.04*25)/(1*25) = (1/25), which is the answer we are looking for.
bottom line:
x = (1/25)
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