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Simplifying ln(3e2) = (9e3) Remove parenthesis around (3e2) ln * 3e2 = (9e3) Reorder the terms for easier multiplication: 3ln * e2 = (9e3) Multiply ln * e2 3e2ln = (9e3) Solving 3e2ln = (9e3) Solving for variable 'e'. Combine like terms: (9e3) + (-9e3) = 0 3e2ln + (-9e3) = 0 Factor out the Greatest Common Factor (GCF), '3e2'. 3e2(ln + (-3e)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'e2' equal to zero and attempt to solve: Simplifying e2 = 0 Solving e2 = 0 Move all terms containing e to the left, all other terms to the right. Simplifying e2 = 0 Take the square root of each side: e = {0}Subproblem 2
Set the factor '(ln + (-3e))' equal to zero and attempt to solve: Simplifying ln + (-3e) = 0 Reorder the terms: (-3e) + ln = 0 Solving (-3e) + ln = 0 Move all terms containing e to the left, all other terms to the right. Add '-1ln' to each side of the equation. (-3e) + ln + -1ln = 0 + -1ln Combine like terms: ln + -1ln = 0 (-3e) + 0 = 0 + -1ln (-3e) = 0 + -1ln Remove the zero: (-3e) = -1ln Divide each side by '-3'. e = 0.3333333333ln Simplifying e = 0.3333333333lnSolution
e = {0, 0.3333333333ln}
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