Troubleshooting a Logarithmic Equation: Seeking Guidance

  • Thread starter MattiasMath
  • Start date
In summary, the conversation was about a person seeking help in solving the equation xlgx = x4/1000. They attempted to solve it using logarithms but got stuck and someone suggested using a quadratic equation in log(x) to find a solution.
  • #1
MattiasMath
5
0
I've run into a dead end trying to solve this equation and I was hoping that someone here might be able to point me in the right direction!

Homework Statement


xlgx = x4/1000

Homework Equations


-

The Attempt at a Solution


xlgx = x4/1000
lg(xlgx) = lg(x4/1000)
(lgx)2 = lg(x4) - lg(1000)
(lgx)2 = 4lgx - 3

Now after this point I'm not sure what to do. I tried:
3 = 4lgx - (lgx)2
3 = lgx * (4 - lgx)

But that doesn't seem to lead me anywhere. Any help would be much appreciated!
 
Last edited:
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  • #2
you have a quadratic equation in [itex]\log(x) [/itex]

let [itex]t=\log(x)[/itex] and solve quadratic equation in t
 
  • #3
Of course, obviously!

Thanks a lot for your help, much appreciated.
 

1. What is a logarithm equation?

A logarithm equation is an equation that involves logarithms, which are mathematical functions that represent the inverse of exponential functions. It is written in the form logb(x) = y, where b is the base, x is the argument, and y is the result.

2. How do you solve a logarithm equation?

To solve a logarithm equation, you can use the properties of logarithms, such as the power rule, product rule, and quotient rule. You can also use exponentiation to eliminate the logarithm and solve for the variable. It is important to check for extraneous solutions and to use the appropriate base when solving.

3. What are the common mistakes when solving logarithm equations?

One common mistake is forgetting to check for extraneous solutions, which are solutions that do not satisfy the original equation. Another mistake is using the wrong base when solving, which can lead to incorrect solutions. It is also important to properly distribute and simplify terms when using logarithmic properties.

4. Can all logarithm equations be solved algebraically?

No, not all logarithm equations can be solved algebraically. Some equations may require the use of a calculator or computer program to find an approximate solution. Additionally, some equations may have no real solutions or an infinite number of solutions.

5. How are logarithm equations used in real-world applications?

Logarithm equations are commonly used in fields such as physics, chemistry, and biology to model exponential growth and decay. They can also be used in finance to calculate compound interest and in engineering to solve problems involving sound and light intensity. Additionally, logarithms are used in computer science and information theory to measure data storage and compression.

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