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Simplifying ln(4x) + -1ln(x + 3) = ln(x2) Remove parenthesis around (4x) ln * 4x + -1ln(x + 3) = ln(x2) Reorder the terms for easier multiplication: 4ln * x + -1ln(x + 3) = ln(x2) Multiply ln * x 4lnx + -1ln(x + 3) = ln(x2) Reorder the terms: 4lnx + -1ln(3 + x) = ln(x2) 4lnx + (3 * -1ln + x * -1ln) = ln(x2) 4lnx + (-3ln + -1lnx) = ln(x2) Reorder the terms: -3ln + 4lnx + -1lnx = ln(x2) Combine like terms: 4lnx + -1lnx = 3lnx -3ln + 3lnx = ln(x2) Multiply ln * x2 -3ln + 3lnx = lnx2 Solving -3ln + 3lnx = lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx2' to each side of the equation. -3ln + 3lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -3ln + 3lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + 3x + -1x2) = 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 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -3 + 3x + -1x2 = 0 Solving -3 + 3x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3x + 3 + -1x2 = 0 + 3 Reorder the terms: -3 + 3 + 3x + -1x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3x + -1x2 = 0 + 3 3x + -1x2 = 0 + 3 Combine like terms: 0 + 3 = 3 3x + -1x2 = 3 Add '-3x' to each side of the equation. 3x + -3x + -1x2 = 3 + -3x Combine like terms: 3x + -3x = 0 0 + -1x2 = 3 + -3x -1x2 = 3 + -3x Add 'x2' to each side of the equation. -1x2 + x2 = 3 + -3x + x2 Combine like terms: -1x2 + x2 = 0 0 = 3 + -3x + x2 Simplifying 0 = 3 + -3x + x2 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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