Asked by Anonymous

log2√36 - log2√72

I am not sure how to do this question. I need an explanation.
Answered by Reiny
You will have to know the 3 prime properties of logs

1. log<sub>k</sub> (AB) = log<sub>k</sub> A + log<sub>k</sub> B
2. log<sub>k</sub>(A/B) = log<sub>k</sub> A - log<sub>k</sub> B
3. log<sub>k</sub> (A^n) = n log<sub>k</sub> A
where k is any positive number , k ≠ 1

so log<sub>2</sub>√36 - log<sub>2</sub> log<sub>2</sub√72
= log<sub>2</sub> (√36/√72)
= log<sub>2</sub> √(36/72)
= log<sub>2</sub> √(1/2)
= log<sub>2</sub> 2^(-1/2)
= (-1/2) log<sub>2</sub> 2
= (-1/2)(1)
= -1/2
Answered by Steve
log(√x) = 1/2 log(x)
since log(x^n) = n log(x)

So, what you have is
√36 = 6, so

√72 = 6√2

So, assuming by log2 you mean log<sub>2</sub>,

log<sub>2</sub>6 + log<sub>2</sub>6 + log<sub>2</sub>2
but log<sub>2</sub>2 = 1, so that is
= 2log<sub>2</sub>6 + 1/2

Now, what is log<sub>2</sub>6?
You don't have a log<sub>2</sub> button on your calculator, but you can easily get it online.

Or, you can change base, remembering that

log<sub>2</sub>6 = log<sub>10</sub>6/log<sub>10</sub>2
Answered by Steve
Oops. I added, instead of subtracting. The final answer, of course, is -1/2, as shown above.
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