Short yet confusing log equation

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Homework Help Overview

The problem involves solving a logarithmic equation that combines multiple logarithmic expressions. The subject area is logarithmic properties and equations.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply logarithmic laws to simplify the equation but expresses confusion about the process. Some participants confirm the validity of using logarithmic properties, while others suggest applying similar rules to both sides of the equation.

Discussion Status

The discussion includes attempts to manipulate the equation into a more manageable form. Some guidance has been offered regarding the application of logarithmic rules, and the original poster has made progress in their reasoning, although they still express uncertainty.

Contextual Notes

There is an indication of confusion regarding the application of logarithmic properties and the simplification process. The original poster's understanding of the laws of logarithms is acknowledged, but they are seeking clarification on their application in this specific case.

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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