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Simplifying ln(y2 + 15) = ln(y + 3) + ln(y) Reorder the terms: ln(15 + y2) = ln(y + 3) + ln(y) (15 * ln + y2 * ln) = ln(y + 3) + ln(y) (15ln + lny2) = ln(y + 3) + ln(y) Reorder the terms: 15ln + lny2 = ln(3 + y) + ln(y) 15ln + lny2 = (3 * ln + y * ln) + ln(y) 15ln + lny2 = (3ln + lny) + ln(y) Multiply ln * y 15ln + lny2 = 3ln + lny + lny Combine like terms: lny + lny = 2lny 15ln + lny2 = 3ln + 2lny Solving 15ln + lny2 = 3ln + 2lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 15ln + -3ln + lny2 = 3ln + -3ln + 2lny Combine like terms: 15ln + -3ln = 12ln 12ln + lny2 = 3ln + -3ln + 2lny Combine like terms: 3ln + -3ln = 0 12ln + lny2 = 0 + 2lny 12ln + lny2 = 2lny Add '-2lny' to each side of the equation. 12ln + -2lny + lny2 = 2lny + -2lny Combine like terms: 2lny + -2lny = 0 12ln + -2lny + lny2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(12 + -2y + y2) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(12 + -2y + y2)' equal to zero and attempt to solve: Simplifying 12 + -2y + y2 = 0 Solving 12 + -2y + y2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -2y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + -2y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -2y + y2 = 0 + -12 -2y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 -2y + y2 = -12 Add '2y' to each side of the equation. -2y + 2y + y2 = -12 + 2y Combine like terms: -2y + 2y = 0 0 + y2 = -12 + 2y y2 = -12 + 2y Add '-1y2' to each side of the equation. y2 + -1y2 = -12 + 2y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -12 + 2y + -1y2 Simplifying 0 = -12 + 2y + -1y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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