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Simplifying ln(5x + 8) = ln(40 + -3x) Reorder the terms: ln(8 + 5x) = ln(40 + -3x) (8 * ln + 5x * ln) = ln(40 + -3x) (8ln + 5lnx) = ln(40 + -3x) 8ln + 5lnx = (40 * ln + -3x * ln) 8ln + 5lnx = (40ln + -3lnx) Solving 8ln + 5lnx = 40ln + -3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-40ln' to each side of the equation. 8ln + -40ln + 5lnx = 40ln + -40ln + -3lnx Combine like terms: 8ln + -40ln = -32ln -32ln + 5lnx = 40ln + -40ln + -3lnx Combine like terms: 40ln + -40ln = 0 -32ln + 5lnx = 0 + -3lnx -32ln + 5lnx = -3lnx Add '3lnx' to each side of the equation. -32ln + 5lnx + 3lnx = -3lnx + 3lnx Combine like terms: 5lnx + 3lnx = 8lnx -32ln + 8lnx = -3lnx + 3lnx Combine like terms: -3lnx + 3lnx = 0 -32ln + 8lnx = 0 Factor out the Greatest Common Factor (GCF), '8ln'. 8ln(-4 + x) = 0 Ignore the factor 8.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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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