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Simplifying ln(6x + 24) = ln(2x + -4) Reorder the terms: ln(24 + 6x) = ln(2x + -4) (24 * ln + 6x * ln) = ln(2x + -4) (24ln + 6lnx) = ln(2x + -4) Reorder the terms: 24ln + 6lnx = ln(-4 + 2x) 24ln + 6lnx = (-4 * ln + 2x * ln) 24ln + 6lnx = (-4ln + 2lnx) Solving 24ln + 6lnx = -4ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4ln' to each side of the equation. 24ln + 4ln + 6lnx = -4ln + 4ln + 2lnx Combine like terms: 24ln + 4ln = 28ln 28ln + 6lnx = -4ln + 4ln + 2lnx Combine like terms: -4ln + 4ln = 0 28ln + 6lnx = 0 + 2lnx 28ln + 6lnx = 2lnx Add '-2lnx' to each side of the equation. 28ln + 6lnx + -2lnx = 2lnx + -2lnx Combine like terms: 6lnx + -2lnx = 4lnx 28ln + 4lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 28ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(7 + x) = 0 Ignore the factor 4.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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -1x 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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