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Simplifying ln(9x + -7) + ln(x + 7) = ln(x + 15) Reorder the terms: ln(-7 + 9x) + ln(x + 7) = ln(x + 15) (-7 * ln + 9x * ln) + ln(x + 7) = ln(x + 15) (-7ln + 9lnx) + ln(x + 7) = ln(x + 15) Reorder the terms: -7ln + 9lnx + ln(7 + x) = ln(x + 15) -7ln + 9lnx + (7 * ln + x * ln) = ln(x + 15) -7ln + 9lnx + (7ln + lnx) = ln(x + 15) Reorder the terms: -7ln + 7ln + 9lnx + lnx = ln(x + 15) Combine like terms: -7ln + 7ln = 0 0 + 9lnx + lnx = ln(x + 15) 9lnx + lnx = ln(x + 15) Combine like terms: 9lnx + lnx = 10lnx 10lnx = ln(x + 15) Reorder the terms: 10lnx = ln(15 + x) 10lnx = (15 * ln + x * ln) 10lnx = (15ln + lnx) Solving 10lnx = 15ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. -15ln + 10lnx = 15ln + -15ln + lnx Combine like terms: 15ln + -15ln = 0 -15ln + 10lnx = 0 + lnx -15ln + 10lnx = lnx Add '-1lnx' to each side of the equation. -15ln + 10lnx + -1lnx = lnx + -1lnx Combine like terms: 10lnx + -1lnx = 9lnx -15ln + 9lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -15ln + 9lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-5 + 3x) = 0 Ignore the factor 3.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 '(-5 + 3x)' equal to zero and attempt to solve: Simplifying -5 + 3x = 0 Solving -5 + 3x = 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 + 3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 0 + 5 3x = 0 + 5 Combine like terms: 0 + 5 = 5 3x = 5 Add '-3x' to each side of the equation. 3x + -3x = 5 + -3x Combine like terms: 3x + -3x = 0 0 = 5 + -3x Simplifying 0 = 5 + -3x 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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