Short yet confusing log equation

AI Thread Summary
The equation log x^4 - log x^3 = log 3x - log 2x can be simplified using logarithmic properties. By applying the quotient rule, it transforms to log(x^4/x^3) = log(3x/2x), which simplifies further to log(x) = log(3/2). The solution reveals that x can be determined by removing the logarithm, leading to x = 3/2. The discussion highlights the effective use of logarithmic laws to solve the equation. Understanding these principles is crucial for tackling similar logarithmic problems.
MadmanMurray
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Homework Statement


Solve the equation
log x4 - log x3 = log 3x - log 2x

I know the laws of logs and I cleared all the other log questions in seconds but I can't figure this one out


Homework Equations


I know that log x4 - log x3 is the same as log x4/x3
but what I was wondering is if I can use the laws of indices here and substract 3 from the 4 leaving me with log x

The Attempt at a Solution


Im completely stuck on this one
 
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Yes you can.
 
Yes, use a similar rule on the other side to solve the equation.
 
I'm still stuck. So I put the equation in this format logx = log(3x/2x) then cancel out those x's so I have logx = log3/2. Do I just get rid of the logs and say x = 3/2?

EDIT: I thought about that there and realized that obviously is the case. Thanks for the help
 
Good Job!
 

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