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Simplifying ln(4 + -5x) = ln(x + 10) (4 * ln + -5x * ln) = ln(x + 10) (4ln + -5lnx) = ln(x + 10) Reorder the terms: 4ln + -5lnx = ln(10 + x) 4ln + -5lnx = (10 * ln + x * ln) 4ln + -5lnx = (10ln + lnx) Solving 4ln + -5lnx = 10ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. 4ln + -10ln + -5lnx = 10ln + -10ln + lnx Combine like terms: 4ln + -10ln = -6ln -6ln + -5lnx = 10ln + -10ln + lnx Combine like terms: 10ln + -10ln = 0 -6ln + -5lnx = 0 + lnx -6ln + -5lnx = lnx Add '-1lnx' to each side of the equation. -6ln + -5lnx + -1lnx = lnx + -1lnx Combine like terms: -5lnx + -1lnx = -6lnx -6ln + -6lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -6ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '-6ln'. -6ln(1 + 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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