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