Solve for x

Problem

ln(x)−ln(x2)+ln(3)=0

Solution

1. Identify the domain of the equation by noting that the argument of a natural logarithm must be positive, so x>0

2. Apply the quotient rule for logarithms, ln(a)−ln(b)=ln(a/b) to the first two terms.

ln(x/(x2))+ln(3)=0

3. Simplify the fraction inside the logarithm.

ln(1/x)+ln(3)=0

4. Apply the product rule for logarithms, ln(a)+ln(b)=ln(a*b) to combine the remaining terms.

ln(3/x)=0

5. Exponentiate both sides using the base e to remove the natural logarithm.

eln(3/x)=e0

3/x=1

6. Solve for x by multiplying both sides by x

3=x

Final Answer

ln(x)−ln(x2)+ln(3)=0⇒x=3

Want more problems? Check here!