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Simplifying 2ln(x) + -1ln(4) = ln(x + 15) Multiply ln * x 2lnx + -1ln(4) = ln(x + 15) Reorder the terms for easier multiplication: 2lnx + -1 * 4ln = ln(x + 15) Multiply -1 * 4 2lnx + -4ln = ln(x + 15) Reorder the terms: -4ln + 2lnx = ln(x + 15) Reorder the terms: -4ln + 2lnx = ln(15 + x) -4ln + 2lnx = (15 * ln + x * ln) -4ln + 2lnx = (15ln + lnx) Solving -4ln + 2lnx = 15ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. -4ln + -15ln + 2lnx = 15ln + -15ln + lnx Combine like terms: -4ln + -15ln = -19ln -19ln + 2lnx = 15ln + -15ln + lnx Combine like terms: 15ln + -15ln = 0 -19ln + 2lnx = 0 + lnx -19ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -19ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -19ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -19ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-19 + 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 '(-19 + x)' equal to zero and attempt to solve: Simplifying -19 + x = 0 Solving -19 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + x = 0 + 19 x = 0 + 19 Combine like terms: 0 + 19 = 19 x = 19 Add '-1x' to each side of the equation. x + -1x = 19 + -1x Combine like terms: x + -1x = 0 0 = 19 + -1x Simplifying 0 = 19 + -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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