We're working with logarithms of base 3

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SUMMARY

The discussion focuses on expressing log(21) in terms of log(4) and log(7), where log(4) is represented as 'a' and log(7) as 'b'. The key insight is recognizing that log(21) can be derived using the properties of logarithms, specifically log(21) = log(3 * 7) = log(3) + log(7). The participant attempted to utilize Matlab for calculations but found it challenging to express 21 as a product or quotient of powers of 7 and 3. The solution involves applying standard logarithmic properties effectively.

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Homework Statement


We're working with logarithms of base 3, and log(4)=a and log(7)=b.
The goal is to put log(21) in terms of a and b. For example, take the log(112). It's the same thing as 2a+b since 4*4*7 = 112.


Homework Equations



Just the standard log properties.

The Attempt at a Solution



The only thing I could come up with is 1 + b log(3) = 1. I've been using Matlab to try to figure out a way to create 21 using a product and/or quotient of powers of 7 and 3 but have been unable to do so.
 
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21 = 3 * 7, and you know log(7) and log(3).
 

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