Is this correct?
Solve:
2lnx-2=0
2lnx=2
Lnex=1
E^1=x
yes.
lne is redundant. ln means log_e. SO, things are a bit clearer if you do it
2lnx = 2
lnx = 1
x = e^1 = e
Thanks! :D
Yes, your steps for solving the equation 2ln(x) - 2 = 0 are correct. Here is another breakdown of the solution process:
1. Start with the equation: 2ln(x) - 2 = 0.
2. Add 2 to both sides of the equation to isolate the natural logarithm term: 2ln(x) = 2.
3. Divide both sides of the equation by 2: ln(x) = 1.
4. Apply the exponential function to both sides of the equation to solve for x. The exponential function "undoes" the natural logarithm function, so we get: e^(ln(x)) = e^1.
5. Simplify the left side using the inverse property of logarithms: x = e^1, or simply x = e.
6. Therefore, the value of x that satisfies the equation 2ln(x) - 2 = 0 is x = e, where e is the mathematical constant approximately equal to 2.71828.
Keep in mind that the solution x = e is only one of the possible solutions. In logarithmic equations, there may be additional solutions that need to be considered.