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Simplifying ln(5x + -7) = ln(8x) + -1ln(2) Reorder the terms: ln(-7 + 5x) = ln(8x) + -1ln(2) (-7 * ln + 5x * ln) = ln(8x) + -1ln(2) (-7ln + 5lnx) = ln(8x) + -1ln(2) Remove parenthesis around (8x) -7ln + 5lnx = ln * 8x + -1ln(2) Reorder the terms for easier multiplication: -7ln + 5lnx = 8ln * x + -1ln(2) Multiply ln * x -7ln + 5lnx = 8lnx + -1ln(2) Reorder the terms for easier multiplication: -7ln + 5lnx = 8lnx + -1 * 2ln Multiply -1 * 2 -7ln + 5lnx = 8lnx + -2ln Reorder the terms: -7ln + 5lnx = -2ln + 8lnx Solving -7ln + 5lnx = -2ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. -7ln + 2ln + 5lnx = -2ln + 2ln + 8lnx Combine like terms: -7ln + 2ln = -5ln -5ln + 5lnx = -2ln + 2ln + 8lnx Combine like terms: -2ln + 2ln = 0 -5ln + 5lnx = 0 + 8lnx -5ln + 5lnx = 8lnx Add '-8lnx' to each side of the equation. -5ln + 5lnx + -8lnx = 8lnx + -8lnx Combine like terms: 5lnx + -8lnx = -3lnx -5ln + -3lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 -5ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(5 + 3x) = 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 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 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 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Add '-3x' to each side of the equation. 3x + -3x = -5 + -3x Combine like terms: 3x + -3x = 0 0 = -5 + -3x Simplifying 0 = -5 + -3x 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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