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Simplifying ln(x) + ln(x + 5) = ln(14) Multiply ln * x lnx + ln(x + 5) = ln(14) Reorder the terms: lnx + ln(5 + x) = ln(14) lnx + (5 * ln + x * ln) = ln(14) lnx + (5ln + lnx) = ln(14) Reorder the terms: 5ln + lnx + lnx = ln(14) Combine like terms: lnx + lnx = 2lnx 5ln + 2lnx = ln(14) Reorder the terms for easier multiplication: 5ln + 2lnx = 14ln Solving 5ln + 2lnx = 14ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. 5ln + -14ln + 2lnx = 14ln + -14ln Combine like terms: 5ln + -14ln = -9ln -9ln + 2lnx = 14ln + -14ln Combine like terms: 14ln + -14ln = 0 -9ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-9 + 2x) = 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 '(-9 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Add '-2x' to each side of the equation. 2x + -2x = 9 + -2x Combine like terms: 2x + -2x = 0 0 = 9 + -2x Simplifying 0 = 9 + -2x 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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