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Simplifying (2x + 13) * ln(2) = (x + -25) * ln(3) Reorder the terms: (13 + 2x) * ln(2) = (x + -25) * ln(3) Reorder the terms for easier multiplication: 2ln(13 + 2x) = (x + -25) * ln(3) (13 * 2ln + 2x * 2ln) = (x + -25) * ln(3) (26ln + 4lnx) = (x + -25) * ln(3) Reorder the terms: 26ln + 4lnx = (-25 + x) * ln(3) Reorder the terms for easier multiplication: 26ln + 4lnx = 3ln(-25 + x) 26ln + 4lnx = (-25 * 3ln + x * 3ln) 26ln + 4lnx = (-75ln + 3lnx) Solving 26ln + 4lnx = -75ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '75ln' to each side of the equation. 26ln + 75ln + 4lnx = -75ln + 75ln + 3lnx Combine like terms: 26ln + 75ln = 101ln 101ln + 4lnx = -75ln + 75ln + 3lnx Combine like terms: -75ln + 75ln = 0 101ln + 4lnx = 0 + 3lnx 101ln + 4lnx = 3lnx Add '-3lnx' to each side of the equation. 101ln + 4lnx + -3lnx = 3lnx + -3lnx Combine like terms: 4lnx + -3lnx = 1lnx 101ln + 1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 101ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(101 + x) = 0Subproblem 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 '(101 + x)' equal to zero and attempt to solve: Simplifying 101 + x = 0 Solving 101 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-101' to each side of the equation. 101 + -101 + x = 0 + -101 Combine like terms: 101 + -101 = 0 0 + x = 0 + -101 x = 0 + -101 Combine like terms: 0 + -101 = -101 x = -101 Add '-1x' to each side of the equation. x + -1x = -101 + -1x Combine like terms: x + -1x = 0 0 = -101 + -1x Simplifying 0 = -101 + -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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