Short yet confusing log equation

In summary, the conversation involved solving the equation log x4 - log x3 = log 3x - log 2x using the laws of logs and indices. The individual was stuck on the solution but eventually realized that the equation can be simplified to x = 3/2.
  • #1
MadmanMurray
76
0

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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  • #2
Yes you can.
 
  • #3
Yes, use a similar rule on the other side to solve the equation.
 
  • #4
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
 
  • #5
Good Job!
 

1. What is a short yet confusing log equation?

A short yet confusing log equation is a mathematical equation that involves logarithmic functions and is relatively short in length, but can be difficult to understand due to its complex nature.

2. How do I solve a short yet confusing log equation?

Solving a short yet confusing log equation involves using the properties of logarithmic functions, such as the product and quotient rules, and simplifying the equation to isolate the variable being solved for. It may also involve using substitution or other algebraic techniques.

3. Why are log equations considered confusing?

Log equations can be confusing because they involve a different way of thinking about numbers and mathematical operations. They also often involve multiple steps and can be difficult to simplify.

4. Can a short yet confusing log equation have multiple solutions?

Yes, a short yet confusing log equation can have multiple solutions. This is because logarithmic functions are not one-to-one, meaning that different inputs can result in the same output.

5. How can I practice and improve my skills in solving short yet confusing log equations?

The best way to practice and improve your skills in solving short yet confusing log equations is to work on a variety of practice problems and seek help from a tutor or teacher if needed. It is also helpful to review the properties and rules of logarithmic functions and to understand the concept behind them.

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