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Simplifying ln(x + 4) = ln(2x) + ln(14) Reorder the terms: ln(4 + x) = ln(2x) + ln(14) (4 * ln + x * ln) = ln(2x) + ln(14) (4ln + lnx) = ln(2x) + ln(14) Remove parenthesis around (2x) 4ln + lnx = ln * 2x + ln(14) Reorder the terms for easier multiplication: 4ln + lnx = 2ln * x + ln(14) Multiply ln * x 4ln + lnx = 2lnx + ln(14) Reorder the terms for easier multiplication: 4ln + lnx = 2lnx + 14ln Reorder the terms: 4ln + lnx = 14ln + 2lnx Solving 4ln + lnx = 14ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. 4ln + -14ln + lnx = 14ln + -14ln + 2lnx Combine like terms: 4ln + -14ln = -10ln -10ln + lnx = 14ln + -14ln + 2lnx Combine like terms: 14ln + -14ln = 0 -10ln + lnx = 0 + 2lnx -10ln + lnx = 2lnx Add '-2lnx' to each side of the equation. -10ln + lnx + -2lnx = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx -10ln + -1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -10ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(10 + x) = 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 '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Add '-1x' to each side of the equation. x + -1x = -10 + -1x Combine like terms: x + -1x = 0 0 = -10 + -1x Simplifying 0 = -10 + -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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