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Simplifying ln(x + -4) = ln(9x) Reorder the terms: ln(-4 + x) = ln(9x) (-4 * ln + x * ln) = ln(9x) (-4ln + lnx) = ln(9x) Remove parenthesis around (9x) -4ln + lnx = ln * 9x Reorder the terms for easier multiplication: -4ln + lnx = 9ln * x Multiply ln * x -4ln + lnx = 9lnx Solving -4ln + lnx = 9lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9lnx' to each side of the equation. -4ln + lnx + -9lnx = 9lnx + -9lnx Combine like terms: lnx + -9lnx = -8lnx -4ln + -8lnx = 9lnx + -9lnx Combine like terms: 9lnx + -9lnx = 0 -4ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), '-4ln'. -4ln(1 + 2x) = 0 Ignore the factor -4.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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -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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