# Algebra 2

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-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.

Assume that
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
e.g.
log2 8 + log2 16
= 3 + 4
= 7
and log2 (8+16)
= log2 24 ≠ 7

Use a similar argument and example for your second question.
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