SOLUTION: log1/2 16 = -4

Question 1091577: log1/2 16 = -4
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If you were not given the answer to

, there is a way to figure out that the answer is .
If you are given that statement

, you can verify/prove that is true by showing that

.

FINDING THE ANSWER:
If you need to calculate logarithms with an cumbersome base ,
you can convert them to a more helpful base , by using the fact that

.
That is a theorem that can be formally proven,
and as a formula is useful, and easy to remember.
Applied to this case, using as your helpful base

.

PROVING GIVEN STATEMENT:
Here is one way to prove that

:
The fraction is divided by ,
and you know that with exponents,
is true, as long as .
So, in this case,

,
and you know that by the definition of negative exponents

,
so

.
You know that
,
and you should know that

If you can think of only as a fraction,
you still would not that the way negative exponents are defined,

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