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Simplifying ln(5x2 + 10) = ln(15x + 20) Reorder the terms: ln(10 + 5x2) = ln(15x + 20) (10 * ln + 5x2 * ln) = ln(15x + 20) (10ln + 5lnx2) = ln(15x + 20) Reorder the terms: 10ln + 5lnx2 = ln(20 + 15x) 10ln + 5lnx2 = (20 * ln + 15x * ln) 10ln + 5lnx2 = (20ln + 15lnx) Solving 10ln + 5lnx2 = 20ln + 15lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-20ln' to each side of the equation. 10ln + -20ln + 5lnx2 = 20ln + -20ln + 15lnx Combine like terms: 10ln + -20ln = -10ln -10ln + 5lnx2 = 20ln + -20ln + 15lnx Combine like terms: 20ln + -20ln = 0 -10ln + 5lnx2 = 0 + 15lnx -10ln + 5lnx2 = 15lnx Add '-15lnx' to each side of the equation. -10ln + -15lnx + 5lnx2 = 15lnx + -15lnx Combine like terms: 15lnx + -15lnx = 0 -10ln + -15lnx + 5lnx2 = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(-2 + -3x + x2) = 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 '(-2 + -3x + x2)' equal to zero and attempt to solve: Simplifying -2 + -3x + x2 = 0 Solving -2 + -3x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -3x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -3x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x + x2 = 0 + 2 -3x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3x + x2 = 2 Add '3x' to each side of the equation. -3x + 3x + x2 = 2 + 3x Combine like terms: -3x + 3x = 0 0 + x2 = 2 + 3x x2 = 2 + 3x Add '-1x2' to each side of the equation. x2 + -1x2 = 2 + 3x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 2 + 3x + -1x2 Simplifying 0 = 2 + 3x + -1x2 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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