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Simplifying ln(4 + -3x) + -1ln(7x) = ln(11) (4 * ln + -3x * ln) + -1ln(7x) = ln(11) (4ln + -3lnx) + -1ln(7x) = ln(11) Remove parenthesis around (7x) 4ln + -3lnx + -1ln * 7x = ln(11) Reorder the terms for easier multiplication: 4ln + -3lnx + -1 * 7ln * x = ln(11) Multiply -1 * 7 4ln + -3lnx + -7ln * x = ln(11) Multiply ln * x 4ln + -3lnx + -7lnx = ln(11) Combine like terms: -3lnx + -7lnx = -10lnx 4ln + -10lnx = ln(11) Reorder the terms for easier multiplication: 4ln + -10lnx = 11ln Solving 4ln + -10lnx = 11ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11ln' to each side of the equation. 4ln + -11ln + -10lnx = 11ln + -11ln Combine like terms: 4ln + -11ln = -7ln -7ln + -10lnx = 11ln + -11ln Combine like terms: 11ln + -11ln = 0 -7ln + -10lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(7 + 10x) = 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 + 10x)' equal to zero and attempt to solve: Simplifying 7 + 10x = 0 Solving 7 + 10x = 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 + 10x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 10x = 0 + -7 10x = 0 + -7 Combine like terms: 0 + -7 = -7 10x = -7 Add '-10x' to each side of the equation. 10x + -10x = -7 + -10x Combine like terms: 10x + -10x = 0 0 = -7 + -10x Simplifying 0 = -7 + -10x 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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