How do you solve ln x=1/2x-1/2?

  • Thread starter johann1301
  • Start date
  • Tags
    Ln
In summary, the conversation is about solving the equation ln x = 1/2x - 1/2 and the importance of using parentheses to clarify mathematical expressions. The person asking for help is reminded to show their own work and provide a clear and readable question.
  • #1
johann1301
217
1
How do you solve ln x=1/2x-1/2?

Please show every step.

Thanks.
 
Physics news on Phys.org
  • #2
We can't help you if you don't shop some work, we're not here to simply show every step of a problem.
 
  • #3
johann1301 said:
How do you solve ln x=1/2x-1/2?

Please show every step.

Thanks.

You need to learn to use parentheses. What you have written reads as
[tex] \ln \, x = \frac{1}{2x} - \frac{1}{2}.[/tex] If that is what you meant, then fine (although you could make it clearer by writing (1/2x) - 1/2 on the right). If you meant to write
[tex] \ln \, x = \frac{1}{2x - 1/2},[/tex] then you need brackets, like this: 1/(2x - 1/2). If you meant something else entirely, you really will have to write it correctly and readably.

And, as others have said, you need to do some of your own work first, and show what you have done.

RGV
 
  • #4
Locked for not providing effort. Feel free to report such threads.
 

FAQ: How do you solve ln x=1/2x-1/2?

What is the first step in solving ln x=1/2x-1/2?

The first step in solving this equation is to isolate the natural logarithm on one side of the equation. We can do this by subtracting 1/2x from both sides, which gives us ln x - 1/2x = -1/2.

How do I solve for x in ln x=1/2x-1/2?

To solve for x, we need to use properties of logarithms. We can rewrite ln x as log base e x. Then, we can use the power rule to rewrite 1/2x as (e^1/2)^x. This gives us log base e x = log base e (e^1/2)^x - 1/2. Now, we can set the exponents equal to each other, giving us x = e^1/2 - 1/2.

Is there another way to solve ln x=1/2x-1/2?

Yes, there is another way to solve this equation. We can use the definition of a logarithm to rewrite ln x as e^(1/2x-1/2). Then, we can use properties of exponents to rewrite e^(1/2x-1/2) as e^(1/2x) / e^(1/2). This gives us x = e^(1/2x) / e^(1/2) = e^(1/2x-1).

Can I use a calculator to solve ln x=1/2x-1/2?

Yes, you can use a calculator to solve this equation. Simply input the expression ln x - 1/2x and solve for x. Many scientific calculators have a log button, which allows you to input the base of the logarithm. In this case, the base is e.

Are there any restrictions on the values of x in ln x=1/2x-1/2?

Yes, there are restrictions on the values of x. Since the natural logarithm is undefined for negative numbers, x must be greater than 0. Additionally, the expression e^(1/2x-1/2) must also be positive in order for the equation to hold true.

Back
Top