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Simplifying ln(x + -7) + ln(x + 3) = ln(24x) Reorder the terms: ln(-7 + x) + ln(x + 3) = ln(24x) (-7 * ln + x * ln) + ln(x + 3) = ln(24x) (-7ln + lnx) + ln(x + 3) = ln(24x) Reorder the terms: -7ln + lnx + ln(3 + x) = ln(24x) -7ln + lnx + (3 * ln + x * ln) = ln(24x) -7ln + lnx + (3ln + lnx) = ln(24x) Reorder the terms: -7ln + 3ln + lnx + lnx = ln(24x) Combine like terms: -7ln + 3ln = -4ln -4ln + lnx + lnx = ln(24x) Combine like terms: lnx + lnx = 2lnx -4ln + 2lnx = ln(24x) Remove parenthesis around (24x) -4ln + 2lnx = ln * 24x Reorder the terms for easier multiplication: -4ln + 2lnx = 24ln * x Multiply ln * x -4ln + 2lnx = 24lnx Solving -4ln + 2lnx = 24lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24lnx' to each side of the equation. -4ln + 2lnx + -24lnx = 24lnx + -24lnx Combine like terms: 2lnx + -24lnx = -22lnx -4ln + -22lnx = 24lnx + -24lnx Combine like terms: 24lnx + -24lnx = 0 -4ln + -22lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(2 + 11x) = 0 Ignore the factor -2.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 '(2 + 11x)' equal to zero and attempt to solve: Simplifying 2 + 11x = 0 Solving 2 + 11x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 11x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 11x = 0 + -2 11x = 0 + -2 Combine like terms: 0 + -2 = -2 11x = -2 Add '-11x' to each side of the equation. 11x + -11x = -2 + -11x Combine like terms: 11x + -11x = 0 0 = -2 + -11x Simplifying 0 = -2 + -11x 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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