posted by Anonymous .
-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 -
Is logb m + logb = logb(m+n)
no they are not, since
logbm + logbn = logb(mn)
All we need is ONE counter-example to show that your statement is false.
logb m + logb = logb(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
log2 8 + log2 16
= 3 + 4
and log2 (8+16)
= log2 24 ≠ 7
Use a similar argument and example for your second question.