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Simplifying ln(x + 5) = ln(11x) Reorder the terms: ln(5 + x) = ln(11x) (5 * ln + x * ln) = ln(11x) (5ln + lnx) = ln(11x) Remove parenthesis around (11x) 5ln + lnx = ln * 11x Reorder the terms for easier multiplication: 5ln + lnx = 11ln * x Multiply ln * x 5ln + lnx = 11lnx Solving 5ln + lnx = 11lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11lnx' to each side of the equation. 5ln + lnx + -11lnx = 11lnx + -11lnx Combine like terms: lnx + -11lnx = -10lnx 5ln + -10lnx = 11lnx + -11lnx Combine like terms: 11lnx + -11lnx = 0 5ln + -10lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(1 + -2x) = 0 Ignore the factor 5.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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