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Simplifying ln(x + 1) + ln(x + -7) = lnx2 Reorder the terms: ln(1 + x) + ln(x + -7) = lnx2 (1 * ln + x * ln) + ln(x + -7) = lnx2 (1ln + lnx) + ln(x + -7) = lnx2 Reorder the terms: 1ln + lnx + ln(-7 + x) = lnx2 1ln + lnx + (-7 * ln + x * ln) = lnx2 1ln + lnx + (-7ln + lnx) = lnx2 Reorder the terms: 1ln + -7ln + lnx + lnx = lnx2 Combine like terms: 1ln + -7ln = -6ln -6ln + lnx + lnx = lnx2 Combine like terms: lnx + lnx = 2lnx -6ln + 2lnx = lnx2 Solving -6ln + 2lnx = lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx2' to each side of the equation. -6ln + 2lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -6ln + 2lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-6 + 2x + -1x2) = 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 '(-6 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -6 + 2x + -1x2 = 0 Solving -6 + 2x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 2x + 6 + -1x2 = 0 + 6 Reorder the terms: -6 + 6 + 2x + -1x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2x + -1x2 = 0 + 6 2x + -1x2 = 0 + 6 Combine like terms: 0 + 6 = 6 2x + -1x2 = 6 Add '-2x' to each side of the equation. 2x + -2x + -1x2 = 6 + -2x Combine like terms: 2x + -2x = 0 0 + -1x2 = 6 + -2x -1x2 = 6 + -2x Add 'x2' to each side of the equation. -1x2 + x2 = 6 + -2x + x2 Combine like terms: -1x2 + x2 = 0 0 = 6 + -2x + x2 Simplifying 0 = 6 + -2x + x2 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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