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How do you simplify #1/2 (log_bM + log_bN - log_bP)#?

Answer 1

Sophie Adams

#= log_b sqrt((MN)/P#

Since our bases are all equal we can use #log_b A + log_b B = log_b(AB)# and #log_b A - log_b B = log_b (A/B)#.

#= 1/2log_b((MN)/P)#

We can now use #alogn = logn^a#.

#= log_b((MN)/P)^(1/2)#

#= log_b sqrt((MN)/P)#

Hopefully this helps!

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Answer 2

Ariana Alvarez

To simplify ( \frac{1}{2} (\log_bM + \log_bN - \log_bP) ), you use the properties of logarithms. The sum of logarithms is equal to the logarithm of the product, and the difference of logarithms is equal to the logarithm of the quotient. So:

( \frac{1}{2} (\log_bM + \log_bN - \log_bP) )

= ( \frac{1}{2} \log_b(M \times N \div P) )

= ( \log_b(\sqrt{MN \div P}) )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.