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Manipulating logs

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By Anonymous on Wednesday, April 11, 2001 - 11:10 pm:

The question is:

If log_a(b)=1/2, evaluate log_a(b^1/2)+log_a(a/b)

Please help!! Thankyou.

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By Brad Rodgers (P1930) on Thursday, April 12, 2001 - 12:01 am:

To solve, first use the property that [1] logm+logn=log(m×n) and get

log_a(a/b^1/2)

Then, from what is given,

b=a^1/2

so

b^1/2=a^1/4

Thus we are looking for

log_a(a^3/4)

using the property that [2] log(mⁿ)=n×log(m), we are finding

3/4×log_a(a)

As [3], log_aa=1, we are given 3/4 as our answer.

In case you haven't yet seen a proof of [1],[2], or [3], just post again, they are easily provable.

Brad

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