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