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johann1301
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How do you solve ln x=1/2x-1/2?
Please show every step.
Thanks.
Please show every step.
Thanks.
johann1301 said:How do you solve ln x=1/2x-1/2?
Please show every step.
Thanks.
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.
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.
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).
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.
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.