Solve \(\ln(x~-~3)~=~4\) by rewriting it in exponential form. Check the domain and verify the result in the original equation.

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Rewrite as x−3=e⁴, so x=e⁴−3. Domain check: x>3, which holds. Equation check: ln(e⁴−6)=4.

Rewrite as x−3=4e, so x=3+4e. Domain check: x>3, which holds. Equation check: ln(4e)=4.

Rewrite as x−3=e⁴, so x=3−e⁴. Domain check: x<3, which is allowed. Equation check: ln(−e⁴)=4.

Rewrite as x−3=e⁴, so x=3+e⁴. Domain check: x>3, which holds. Equation check: ln(e⁴)=4.

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Curriculum context

Course: Math III
Standard: F-IF.8
Category: Functions
Domain: Interpreting Functions
Objective: Rewrite functions in equivalent forms to reveal and explain useful properties.
Problem type: Rewrite to a specified solvable form and finish the solution