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Simplifying ln(4 + x2) = ln(x) + 2ln(2) (4 * ln + x2 * ln) = ln(x) + 2ln(2) (4ln + lnx2) = ln(x) + 2ln(2) Multiply ln * x 4ln + lnx2 = lnx + 2ln(2) Reorder the terms for easier multiplication: 4ln + lnx2 = lnx + 2 * 2ln Multiply 2 * 2 4ln + lnx2 = lnx + 4ln Reorder the terms: 4ln + lnx2 = 4ln + lnx Add '-4ln' to each side of the equation. 4ln + -4ln + lnx2 = 4ln + -4ln + lnx Combine like terms: 4ln + -4ln = 0 0 + lnx2 = 4ln + -4ln + lnx lnx2 = 4ln + -4ln + lnx Combine like terms: 4ln + -4ln = 0 lnx2 = 0 + lnx lnx2 = lnx Solving lnx2 = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. -1lnx + lnx2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -1lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'lnx'. lnx(-1 + x) = 0Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve: Simplifying lnx = 0 Solving lnx = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx = 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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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