SOLUTION: if log7 = m and log5 = n write the following in terms of n and m a) log3500 b)log2

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Question 1180282: if log7 = m and log5 = n write the following in terms of n and m
a) log3500
b)log2
Found 2 solutions by greenestamps, Boreal:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Since a base is not specified, the base is 10.

a) log(3500)

3500=(5)(7)(10^2)
log(3500)=log(5)+log(7)+2log(10) = log(5)+log(7)+2

b) log(2)

2 =10/5
log(2)=log(10)-log(5)=1-log(5)

Use the given definitions of m and n to write the two logs in terms of m and n.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
log 3500=log 7+log 500=log 7+log(5*100)=log 7+log 5+2=2+n+m
log 2 is log (10/5) or log 10-log 5 or 1-n