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Simplifying ln(x + -7) + ln(x + 9) = ln(36) Reorder the terms: ln(-7 + x) + ln(x + 9) = ln(36) (-7 * ln + x * ln) + ln(x + 9) = ln(36) (-7ln + lnx) + ln(x + 9) = ln(36) Reorder the terms: -7ln + lnx + ln(9 + x) = ln(36) -7ln + lnx + (9 * ln + x * ln) = ln(36) -7ln + lnx + (9ln + lnx) = ln(36) Reorder the terms: -7ln + 9ln + lnx + lnx = ln(36) Combine like terms: -7ln + 9ln = 2ln 2ln + lnx + lnx = ln(36) Combine like terms: lnx + lnx = 2lnx 2ln + 2lnx = ln(36) Reorder the terms for easier multiplication: 2ln + 2lnx = 36ln Solving 2ln + 2lnx = 36ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-36ln' to each side of the equation. 2ln + -36ln + 2lnx = 36ln + -36ln Combine like terms: 2ln + -36ln = -34ln -34ln + 2lnx = 36ln + -36ln Combine like terms: 36ln + -36ln = 0 -34ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-17 + x) = 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 '(-17 + x)' equal to zero and attempt to solve: Simplifying -17 + x = 0 Solving -17 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + x = 0 + 17 x = 0 + 17 Combine like terms: 0 + 17 = 17 x = 17 Add '-1x' to each side of the equation. x + -1x = 17 + -1x Combine like terms: x + -1x = 0 0 = 17 + -1x Simplifying 0 = 17 + -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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