Solve for x natural log of x^2-1=3

Problem

ln(x2−1)=3

Solution

1. Rewrite the equation in exponential form by applying the base e to both sides to remove the natural logarithm.

ln(x2−1)=3

x2−1=e3

2. Isolate the x2 term by adding 1 to both sides of the equation.

x2=e3+1

3. Solve for x by taking the square root of both sides, remembering to include both the positive and negative roots.

x=±√(,e3+1)

Final Answer

ln(x2−1)=3⇒x=±√(,e3+1)

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