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Simplifying ln(x + 2) + ln(x + 3) = ln(10x + 20) Reorder the terms: ln(2 + x) + ln(x + 3) = ln(10x + 20) (2 * ln + x * ln) + ln(x + 3) = ln(10x + 20) (2ln + lnx) + ln(x + 3) = ln(10x + 20) Reorder the terms: 2ln + lnx + ln(3 + x) = ln(10x + 20) 2ln + lnx + (3 * ln + x * ln) = ln(10x + 20) 2ln + lnx + (3ln + lnx) = ln(10x + 20) Reorder the terms: 2ln + 3ln + lnx + lnx = ln(10x + 20) Combine like terms: 2ln + 3ln = 5ln 5ln + lnx + lnx = ln(10x + 20) Combine like terms: lnx + lnx = 2lnx 5ln + 2lnx = ln(10x + 20) Reorder the terms: 5ln + 2lnx = ln(20 + 10x) 5ln + 2lnx = (20 * ln + 10x * ln) 5ln + 2lnx = (20ln + 10lnx) Solving 5ln + 2lnx = 20ln + 10lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-20ln' to each side of the equation. 5ln + -20ln + 2lnx = 20ln + -20ln + 10lnx Combine like terms: 5ln + -20ln = -15ln -15ln + 2lnx = 20ln + -20ln + 10lnx Combine like terms: 20ln + -20ln = 0 -15ln + 2lnx = 0 + 10lnx -15ln + 2lnx = 10lnx Add '-10lnx' to each side of the equation. -15ln + 2lnx + -10lnx = 10lnx + -10lnx Combine like terms: 2lnx + -10lnx = -8lnx -15ln + -8lnx = 10lnx + -10lnx Combine like terms: 10lnx + -10lnx = 0 -15ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(15 + 8x) = 0 Ignore the factor -1.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 '(15 + 8x)' equal to zero and attempt to solve: Simplifying 15 + 8x = 0 Solving 15 + 8x = 0 Move all terms containing l to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 8x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 8x = 0 + -15 8x = 0 + -15 Combine like terms: 0 + -15 = -15 8x = -15 Add '-8x' to each side of the equation. 8x + -8x = -15 + -8x Combine like terms: 8x + -8x = 0 0 = -15 + -8x Simplifying 0 = -15 + -8x 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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