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Simplifying ln(x + 3) + ln(x) = ln(11x + -15) Reorder the terms: ln(3 + x) + ln(x) = ln(11x + -15) (3 * ln + x * ln) + ln(x) = ln(11x + -15) (3ln + lnx) + ln(x) = ln(11x + -15) Multiply ln * x 3ln + lnx + lnx = ln(11x + -15) Combine like terms: lnx + lnx = 2lnx 3ln + 2lnx = ln(11x + -15) Reorder the terms: 3ln + 2lnx = ln(-15 + 11x) 3ln + 2lnx = (-15 * ln + 11x * ln) 3ln + 2lnx = (-15ln + 11lnx) Solving 3ln + 2lnx = -15ln + 11lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '15ln' to each side of the equation. 3ln + 15ln + 2lnx = -15ln + 15ln + 11lnx Combine like terms: 3ln + 15ln = 18ln 18ln + 2lnx = -15ln + 15ln + 11lnx Combine like terms: -15ln + 15ln = 0 18ln + 2lnx = 0 + 11lnx 18ln + 2lnx = 11lnx Add '-11lnx' to each side of the equation. 18ln + 2lnx + -11lnx = 11lnx + -11lnx Combine like terms: 2lnx + -11lnx = -9lnx 18ln + -9lnx = 11lnx + -11lnx Combine like terms: 11lnx + -11lnx = 0 18ln + -9lnx = 0 Factor out the Greatest Common Factor (GCF), '9ln'. 9ln(2 + -1x) = 0 Ignore the factor 9.Subproblem 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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