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Simplifying ln(x + 5) + ln(10 + -1x) = ln(32 + -1x) Reorder the terms: ln(5 + x) + ln(10 + -1x) = ln(32 + -1x) (5 * ln + x * ln) + ln(10 + -1x) = ln(32 + -1x) (5ln + lnx) + ln(10 + -1x) = ln(32 + -1x) 5ln + lnx + (10 * ln + -1x * ln) = ln(32 + -1x) 5ln + lnx + (10ln + -1lnx) = ln(32 + -1x) Reorder the terms: 5ln + 10ln + lnx + -1lnx = ln(32 + -1x) Combine like terms: 5ln + 10ln = 15ln 15ln + lnx + -1lnx = ln(32 + -1x) Combine like terms: lnx + -1lnx = 0 15ln + 0 = ln(32 + -1x) 15ln = ln(32 + -1x) 15ln = (32 * ln + -1x * ln) 15ln = (32ln + -1lnx) Solving 15ln = 32ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-32ln' to each side of the equation. 15ln + -32ln = 32ln + -32ln + -1lnx Combine like terms: 15ln + -32ln = -17ln -17ln = 32ln + -32ln + -1lnx Combine like terms: 32ln + -32ln = 0 -17ln = 0 + -1lnx -17ln = -1lnx Add 'lnx' to each side of the equation. -17ln + lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -17ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-17 + 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 '(-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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