Posted by **Anonymous** on Saturday, July 20, 2013 at 5:24pm.

-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**, Saturday, July 20, 2013 at 10:54pm
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 counter-example 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.

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