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Simplifying Ln(3) + -1ln(x + 5) = ln(x) Reorder the terms for easier multiplication: 3nL + -1ln(x + 5) = ln(x) Reorder the terms: 3nL + -1ln(5 + x) = ln(x) 3nL + (5 * -1ln + x * -1ln) = ln(x) 3nL + (-5ln + -1lnx) = ln(x) Reorder the terms: -5ln + -1lnx + 3nL = ln(x) Multiply ln * x -5ln + -1lnx + 3nL = lnx Solving -5ln + -1lnx + 3nL = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. -5ln + -1lnx + -1lnx + 3nL = lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx -5ln + -2lnx + 3nL = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -5ln + -2lnx + 3nL = 0 Add '-3nL' to each side of the equation. -5ln + -2lnx + 3nL + -3nL = 0 + -3nL Combine like terms: 3nL + -3nL = 0 -5ln + -2lnx + 0 = 0 + -3nL -5ln + -2lnx = 0 + -3nL Remove the zero: -5ln + -2lnx = -3nL Combine like terms: -3nL + 3nL = 0 -5ln + -2lnx + 3nL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-5l + -2lx + 3L) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(-5l + -2lx + 3L)' equal to zero and attempt to solve: Simplifying -5l + -2lx + 3L = 0 Reorder the terms: 3L + -5l + -2lx = 0 Solving 3L + -5l + -2lx = 0 Move all terms containing l to the left, all other terms to the right. Add '-3L' to each side of the equation. 3L + -5l + -3L + -2lx = 0 + -3L Reorder the terms: 3L + -3L + -5l + -2lx = 0 + -3L Combine like terms: 3L + -3L = 0 0 + -5l + -2lx = 0 + -3L -5l + -2lx = 0 + -3L Remove the zero: -5l + -2lx = -3L 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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