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Simplifying ln(x2 + 1) = ln(6x + 1) Reorder the terms: ln(1 + x2) = ln(6x + 1) (1 * ln + x2 * ln) = ln(6x + 1) (1ln + lnx2) = ln(6x + 1) Reorder the terms: 1ln + lnx2 = ln(1 + 6x) 1ln + lnx2 = (1 * ln + 6x * ln) 1ln + lnx2 = (1ln + 6lnx) Add '-1ln' to each side of the equation. 1ln + -1ln + lnx2 = 1ln + -1ln + 6lnx Combine like terms: 1ln + -1ln = 0 0 + lnx2 = 1ln + -1ln + 6lnx lnx2 = 1ln + -1ln + 6lnx Combine like terms: 1ln + -1ln = 0 lnx2 = 0 + 6lnx lnx2 = 6lnx Solving lnx2 = 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6lnx' to each side of the equation. -6lnx + lnx2 = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -6lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'lnx'. lnx(-6 + 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -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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