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Simplifying ln(1 + -1x) + ln(4 + -1x) = ln(10) (1 * ln + -1x * ln) + ln(4 + -1x) = ln(10) (1ln + -1lnx) + ln(4 + -1x) = ln(10) 1ln + -1lnx + (4 * ln + -1x * ln) = ln(10) 1ln + -1lnx + (4ln + -1lnx) = ln(10) Reorder the terms: 1ln + 4ln + -1lnx + -1lnx = ln(10) Combine like terms: 1ln + 4ln = 5ln 5ln + -1lnx + -1lnx = ln(10) Combine like terms: -1lnx + -1lnx = -2lnx 5ln + -2lnx = ln(10) Reorder the terms for easier multiplication: 5ln + -2lnx = 10ln Solving 5ln + -2lnx = 10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. 5ln + -10ln + -2lnx = 10ln + -10ln Combine like terms: 5ln + -10ln = -5ln -5ln + -2lnx = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -5ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(5 + 2x) = 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 '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Add '-2x' to each side of the equation. 2x + -2x = -5 + -2x Combine like terms: 2x + -2x = 0 0 = -5 + -2x Simplifying 0 = -5 + -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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