Solve for x natural log of 2x-1=0

Problem

ln(2*x−1)=0

Solution

1. Identify the logarithmic equation and the base of the natural logarithm, which is e

2. Rewrite the equation in exponential form by applying the property ln(y)=a⇔y=ea

2*x−1=e0

3. Simplify the right side of the equation using the property that any non-zero number raised to the power of 0 is 1

2*x−1=1

4. Isolate the term containing x by adding 1 to both sides of the equation.

2*x=2

5. Solve for x by dividing both sides by 2

x=1

6. Verify the solution by substituting x=1 back into the original expression to ensure the argument of the logarithm is positive.

ln(2*(1)−1)=ln(1)=0

Final Answer

ln(2*x−1)=0⇒x=1

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