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Simplifying ln(x + 6) + ln(x) = ln(x + 24) Reorder the terms: ln(6 + x) + ln(x) = ln(x + 24) (6 * ln + x * ln) + ln(x) = ln(x + 24) (6ln + lnx) + ln(x) = ln(x + 24) Multiply ln * x 6ln + lnx + lnx = ln(x + 24) Combine like terms: lnx + lnx = 2lnx 6ln + 2lnx = ln(x + 24) Reorder the terms: 6ln + 2lnx = ln(24 + x) 6ln + 2lnx = (24 * ln + x * ln) 6ln + 2lnx = (24ln + lnx) Solving 6ln + 2lnx = 24ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. 6ln + -24ln + 2lnx = 24ln + -24ln + lnx Combine like terms: 6ln + -24ln = -18ln -18ln + 2lnx = 24ln + -24ln + lnx Combine like terms: 24ln + -24ln = 0 -18ln + 2lnx = 0 + lnx -18ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -18ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -18ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -18ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-18 + 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 '(-18 + x)' equal to zero and attempt to solve: Simplifying -18 + x = 0 Solving -18 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 0 + 18 Combine like terms: -18 + 18 = 0 0 + x = 0 + 18 x = 0 + 18 Combine like terms: 0 + 18 = 18 x = 18 Add '-1x' to each side of the equation. x + -1x = 18 + -1x Combine like terms: x + -1x = 0 0 = 18 + -1x Simplifying 0 = 18 + -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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