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Simplifying ln(4x5 + 3x) = ln(x) + ln(3) Reorder the terms: ln(3x + 4x5) = ln(x) + ln(3) (3x * ln + 4x5 * ln) = ln(x) + ln(3) (3lnx + 4lnx5) = ln(x) + ln(3) Multiply ln * x 3lnx + 4lnx5 = lnx + ln(3) Reorder the terms for easier multiplication: 3lnx + 4lnx5 = lnx + 3ln Reorder the terms: 3lnx + 4lnx5 = 3ln + lnx Solving 3lnx + 4lnx5 = 3ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 3lnx + -3ln + 4lnx5 = 3ln + -3ln + lnx Reorder the terms: -3ln + 3lnx + 4lnx5 = 3ln + -3ln + lnx Combine like terms: 3ln + -3ln = 0 -3ln + 3lnx + 4lnx5 = 0 + lnx -3ln + 3lnx + 4lnx5 = lnx Add '-1lnx' to each side of the equation. -3ln + 3lnx + -1lnx + 4lnx5 = lnx + -1lnx Combine like terms: 3lnx + -1lnx = 2lnx -3ln + 2lnx + 4lnx5 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -3ln + 2lnx + 4lnx5 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + 2x + 4x5) = 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 '(-3 + 2x + 4x5)' equal to zero and attempt to solve: Simplifying -3 + 2x + 4x5 = 0 Solving -3 + 2x + 4x5 = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 2x + 3 + 4x5 = 0 + 3 Reorder the terms: -3 + 3 + 2x + 4x5 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x + 4x5 = 0 + 3 2x + 4x5 = 0 + 3 Combine like terms: 0 + 3 = 3 2x + 4x5 = 3 Add '-2x' to each side of the equation. 2x + -2x + 4x5 = 3 + -2x Combine like terms: 2x + -2x = 0 0 + 4x5 = 3 + -2x 4x5 = 3 + -2x Add '-4x5' to each side of the equation. 4x5 + -4x5 = 3 + -2x + -4x5 Combine like terms: 4x5 + -4x5 = 0 0 = 3 + -2x + -4x5 Simplifying 0 = 3 + -2x + -4x5 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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