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Simplifying ln(x + -5) = ln(10x) Reorder the terms: ln(-5 + x) = ln(10x) (-5 * ln + x * ln) = ln(10x) (-5ln + lnx) = ln(10x) Remove parenthesis around (10x) -5ln + lnx = ln * 10x Reorder the terms for easier multiplication: -5ln + lnx = 10ln * x Multiply ln * x -5ln + lnx = 10lnx Solving -5ln + lnx = 10lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10lnx' to each side of the equation. -5ln + lnx + -10lnx = 10lnx + -10lnx Combine like terms: lnx + -10lnx = -9lnx -5ln + -9lnx = 10lnx + -10lnx Combine like terms: 10lnx + -10lnx = 0 -5ln + -9lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(5 + 9x) = 0 Ignore the factor -1.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 '(5 + 9x)' equal to zero and attempt to solve: Simplifying 5 + 9x = 0 Solving 5 + 9x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 9x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 9x = 0 + -5 9x = 0 + -5 Combine like terms: 0 + -5 = -5 9x = -5 Add '-9x' to each side of the equation. 9x + -9x = -5 + -9x Combine like terms: 9x + -9x = 0 0 = -5 + -9x Simplifying 0 = -5 + -9x 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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