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