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Simplifying ln(3x + 13) + -1ln(x) = ln4 Reorder the terms: ln(13 + 3x) + -1ln(x) = ln4 (13 * ln + 3x * ln) + -1ln(x) = ln4 (13ln + 3lnx) + -1ln(x) = ln4 Multiply ln * x 13ln + 3lnx + -1lnx = ln4 Combine like terms: 3lnx + -1lnx = 2lnx 13ln + 2lnx = ln4 Solving 13ln + 2lnx = ln4 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln4' to each side of the equation. 13ln + 2lnx + -1ln4 = ln4 + -1ln4 Combine like terms: ln4 + -1ln4 = 0 13ln + 2lnx + -1ln4 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(13 + 2x + -1n3) = 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 '(13 + 2x + -1n3)' equal to zero and attempt to solve: Simplifying 13 + 2x + -1n3 = 0 Reorder the terms: 13 + -1n3 + 2x = 0 Solving 13 + -1n3 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -1n3 + -13 + 2x = 0 + -13 Reorder the terms: 13 + -13 + -1n3 + 2x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1n3 + 2x = 0 + -13 -1n3 + 2x = 0 + -13 Combine like terms: 0 + -13 = -13 -1n3 + 2x = -13 Add 'n3' to each side of the equation. -1n3 + n3 + 2x = -13 + n3 Combine like terms: -1n3 + n3 = 0 0 + 2x = -13 + n3 2x = -13 + n3 Add '-2x' to each side of the equation. 2x + -2x = -13 + n3 + -2x Combine like terms: 2x + -2x = 0 0 = -13 + n3 + -2x Simplifying 0 = -13 + n3 + -2x 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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