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Simplifying ln(x + 2) = ln(25) + ln(5x + -2) Reorder the terms: ln(2 + x) = ln(25) + ln(5x + -2) (2 * ln + x * ln) = ln(25) + ln(5x + -2) (2ln + lnx) = ln(25) + ln(5x + -2) Reorder the terms for easier multiplication: 2ln + lnx = 25ln + ln(5x + -2) Reorder the terms: 2ln + lnx = 25ln + ln(-2 + 5x) 2ln + lnx = 25ln + (-2 * ln + 5x * ln) 2ln + lnx = 25ln + (-2ln + 5lnx) Combine like terms: 25ln + -2ln = 23ln 2ln + lnx = 23ln + 5lnx Solving 2ln + lnx = 23ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-23ln' to each side of the equation. 2ln + -23ln + lnx = 23ln + -23ln + 5lnx Combine like terms: 2ln + -23ln = -21ln -21ln + lnx = 23ln + -23ln + 5lnx Combine like terms: 23ln + -23ln = 0 -21ln + lnx = 0 + 5lnx -21ln + lnx = 5lnx Add '-5lnx' to each side of the equation. -21ln + lnx + -5lnx = 5lnx + -5lnx Combine like terms: lnx + -5lnx = -4lnx -21ln + -4lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -21ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(21 + 4x) = 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 '(21 + 4x)' equal to zero and attempt to solve: Simplifying 21 + 4x = 0 Solving 21 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 4x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 4x = 0 + -21 4x = 0 + -21 Combine like terms: 0 + -21 = -21 4x = -21 Add '-4x' to each side of the equation. 4x + -4x = -21 + -4x Combine like terms: 4x + -4x = 0 0 = -21 + -4x Simplifying 0 = -21 + -4x 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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