Logarithmic Help: Solving for z, m & n

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The discussion focuses on solving for variables z, m, and n using logarithmic properties in a homework problem. The initial attempts successfully calculated some values using the logarithm of 2 and 1.1, but similar methods failed for the remaining variables. Participants suggest approximating numbers like 2 and 3 as powers of 1.1, specifically 1.1^N and 1.1^M. The exercise emphasizes understanding the relationship between exponential and logarithmic forms to derive the correct values. Overall, the key is to apply logarithmic properties consistently to find the desired solutions.
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Homework Statement



http://img20.imageshack.us/img20/1476/mathproblemi.jpg


Homework Equations



Properties of logs.

The Attempt at a Solution



For the first two I did:

Int( \frac{Log(2)}{Log(1.1)} )

Doing this resulted in the correct answers for the first two boxes. When I try similar techniques to solve for z, m,n I get incorrect answers.

Anyone have tips or suggestions on how to go about finding these?
 
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Your task is to approximate 2 and 3 as 1.1^N and 1.1^M, and solve z from there.
 
If 1.1^7 is approximately 2 then 2^x is approximately (1.1^7)^x= 1.1^{7x}. That's the point of this exercise.
 

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