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# TRUE OR FALSE PLS HELP

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loga(u+v)=loga (u)+loga(v)

Mar 25, 2020

#1
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Let's use an example for this:

log(3)= 0.47712125472

log(6)= 0.77815125038

log(9)= 0.95424250943

Therefore, this is FALSE.

Hope this helped!

Mar 25, 2020
#2
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+2

Hey mharrigan! In this problem, we'll make use of a useful log identity.

\(\log_{a}b + \log_ac = \log_{a}bc\)

Given that these two logs have the same base.

As such, since we have:

\(\log_au + \log_av\), we can rewrite this to equal:

\(\log_au + \log_av = \log_a{uv}\)

This is where the question becomes kind of murky. The problem itself never says what "true or false" means in the context of the problem. Does it mean for all u and v, or just find one u and v so that it satisfies that requirement? Meaning that for all we know, uv could equal u + v(we don't know, it never says?). Contrary to Cal's answer, if the problem asked you to find one such case so that this expression holds true, then the answer would be true(we can have 2 and 2, which would work). However, if it was in general, then it would be definitely false.

Mar 26, 2020