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Simplifying ln(5x) = ln(24 + -1x) Remove parenthesis around (5x) ln * 5x = ln(24 + -1x) Reorder the terms for easier multiplication: 5ln * x = ln(24 + -1x) Multiply ln * x 5lnx = ln(24 + -1x) 5lnx = (24 * ln + -1x * ln) 5lnx = (24ln + -1lnx) Solving 5lnx = 24ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. -24ln + 5lnx = 24ln + -24ln + -1lnx Combine like terms: 24ln + -24ln = 0 -24ln + 5lnx = 0 + -1lnx -24ln + 5lnx = -1lnx Add 'lnx' to each side of the equation. -24ln + 5lnx + lnx = -1lnx + lnx Combine like terms: 5lnx + lnx = 6lnx -24ln + 6lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -24ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '6ln'. 6ln(-4 + x) = 0 Ignore the factor 6.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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -1x 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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