Posted by Anonymous on .
Explain the difference between log base b of m plus log base b of n and log base b (m+n). Are they equivalent?
Explain the difference between log base b (mn) and ( log base b of m)(log base b of n). Are they equivalent?

Algebra 2 
Reiny,
Is log_{b} m + log_{b} = log_{b}(m+n)
no they are not, since
log_{b}m + log_{b}n = log_{b}(mn)
All we need is ONE counterexample to show that your statement is false.
Assume that
log_{b} m + log_{b} = log_{b}(m+n)
then it should be true for all values of b, m, and n within the domain of log definitions.
let's take some values for which we know the exact values
e.g.
log_{2} 8 + log_{2} 16
= 3 + 4
= 7
and log_{2} (8+16)
= log_{2} 24 ≠ 7
Use a similar argument and example for your second question.