We're working with logarithms of base 3

[tharock220]

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.

 

[SammyS]

21 = 3 * 7, and you know log(7) and log(3).