SOLUTION: Given that log6 base 3=m and log 5 base 6=n. Express log 10 base 3 in terms of m and n

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Question 1145291: Given that log6 base 3=m and log 5 base 6=n. Express log 10 base 3 in terms of m and n
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52818)   (Show Source): You can put this solution on YOUR website!
.
Since 10 = 2*5, you have 

 =  =  + .    (1)



 is given to you as the value  n = .



Your task is to retrieve    from the given data.


It is simple:  m =  =  =  +  =  + 1;

hence,   = m-1.


Therefore, from the formula (1)   = (m-1) + n = m + n - 1.    ANSWER

Solved.

----------------

Edwin,  thanks for noticing my error !

I was in hurry and mistakenly read  "log 5 base 6"  as   .



Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
I'm sorry, Ikleyn, but the above is incorrect.

    

We substitute 3m-1 for 2 in 2n3n = 5.



We multiply equations 3m-1 = 2 and 3mn= 5.



Edwin
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