Asked 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?
-Explain the difference between log base b (mn) and ( log base b of m)(log base b of n). Are they equivalent?
Answers
Answered by
Reiny
Is log<sub>b</sub> m + log<sub>b</sub> = log<sub>b</sub>(m+n)
no they are not, since
log<sub>b</sub>m + log<sub>b</sub>n = log<sub>b</sub>(mn)
All we need is ONE counter-example to show that your statement is false.
Assume that
log<sub>b</sub> m + log<sub>b</sub> = log<sub>b</sub>(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<sub>2</sub> 8 + log<sub>2</sub> 16
= 3 + 4
= 7
and log<sub>2</sub> (8+16)
= log<sub>2</sub> 24 ≠ 7
Use a similar argument and example for your second question.
no they are not, since
log<sub>b</sub>m + log<sub>b</sub>n = log<sub>b</sub>(mn)
All we need is ONE counter-example to show that your statement is false.
Assume that
log<sub>b</sub> m + log<sub>b</sub> = log<sub>b</sub>(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<sub>2</sub> 8 + log<sub>2</sub> 16
= 3 + 4
= 7
and log<sub>2</sub> (8+16)
= log<sub>2</sub> 24 ≠ 7
Use a similar argument and example for your second question.
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