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Simplifying ln(x) + ln(x + -4) = ln(x + 6) Multiply ln * x lnx + ln(x + -4) = ln(x + 6) Reorder the terms: lnx + ln(-4 + x) = ln(x + 6) lnx + (-4 * ln + x * ln) = ln(x + 6) lnx + (-4ln + lnx) = ln(x + 6) Reorder the terms: -4ln + lnx + lnx = ln(x + 6) Combine like terms: lnx + lnx = 2lnx -4ln + 2lnx = ln(x + 6) Reorder the terms: -4ln + 2lnx = ln(6 + x) -4ln + 2lnx = (6 * ln + x * ln) -4ln + 2lnx = (6ln + lnx) Solving -4ln + 2lnx = 6ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. -4ln + -6ln + 2lnx = 6ln + -6ln + lnx Combine like terms: -4ln + -6ln = -10ln -10ln + 2lnx = 6ln + -6ln + lnx Combine like terms: 6ln + -6ln = 0 -10ln + 2lnx = 0 + lnx -10ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -10ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -10ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -10ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + x) = 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 '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Add '-1x' to each side of the equation. x + -1x = 10 + -1x Combine like terms: x + -1x = 0 0 = 10 + -1x Simplifying 0 = 10 + -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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