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Simplifying ln(x) = 4ln(2x) + -2ln(x + -1) + ln(5) Multiply ln * x lnx = 4ln(2x) + -2ln(x + -1) + ln(5) Remove parenthesis around (2x) lnx = 4ln * 2x + -2ln(x + -1) + ln(5) Reorder the terms for easier multiplication: lnx = 4 * 2ln * x + -2ln(x + -1) + ln(5) Multiply 4 * 2 lnx = 8ln * x + -2ln(x + -1) + ln(5) Multiply ln * x lnx = 8lnx + -2ln(x + -1) + ln(5) Reorder the terms: lnx = 8lnx + -2ln(-1 + x) + ln(5) lnx = 8lnx + (-1 * -2ln + x * -2ln) + ln(5) lnx = 8lnx + (2ln + -2lnx) + ln(5) Reorder the terms for easier multiplication: lnx = 8lnx + 2ln + -2lnx + 5ln Reorder the terms: lnx = 2ln + 5ln + 8lnx + -2lnx Combine like terms: 2ln + 5ln = 7ln lnx = 7ln + 8lnx + -2lnx Combine like terms: 8lnx + -2lnx = 6lnx lnx = 7ln + 6lnx Solving lnx = 7ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. -7ln + lnx = 7ln + -7ln + 6lnx Combine like terms: 7ln + -7ln = 0 -7ln + lnx = 0 + 6lnx -7ln + lnx = 6lnx Add '-6lnx' to each side of the equation. -7ln + lnx + -6lnx = 6lnx + -6lnx Combine like terms: lnx + -6lnx = -5lnx -7ln + -5lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -7ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(7 + 5x) = 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 '(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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