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Simplifying ln(x + -4) + ln(2x + -1) = ln(18x) Reorder the terms: ln(-4 + x) + ln(2x + -1) = ln(18x) (-4 * ln + x * ln) + ln(2x + -1) = ln(18x) (-4ln + lnx) + ln(2x + -1) = ln(18x) Reorder the terms: -4ln + lnx + ln(-1 + 2x) = ln(18x) -4ln + lnx + (-1 * ln + 2x * ln) = ln(18x) -4ln + lnx + (-1ln + 2lnx) = ln(18x) Reorder the terms: -4ln + -1ln + lnx + 2lnx = ln(18x) Combine like terms: -4ln + -1ln = -5ln -5ln + lnx + 2lnx = ln(18x) Combine like terms: lnx + 2lnx = 3lnx -5ln + 3lnx = ln(18x) Remove parenthesis around (18x) -5ln + 3lnx = ln * 18x Reorder the terms for easier multiplication: -5ln + 3lnx = 18ln * x Multiply ln * x -5ln + 3lnx = 18lnx Solving -5ln + 3lnx = 18lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18lnx' to each side of the equation. -5ln + 3lnx + -18lnx = 18lnx + -18lnx Combine like terms: 3lnx + -18lnx = -15lnx -5ln + -15lnx = 18lnx + -18lnx Combine like terms: 18lnx + -18lnx = 0 -5ln + -15lnx = 0 Factor out the Greatest Common Factor (GCF), '-5ln'. -5ln(1 + 3x) = 0 Ignore the factor -5.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 '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Add '-3x' to each side of the equation. 3x + -3x = -1 + -3x Combine like terms: 3x + -3x = 0 0 = -1 + -3x Simplifying 0 = -1 + -3x 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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