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Simplifying ln(x + -3)[ln(x + -5) + ln(x + 5)] = 0 Reorder the terms: ln(-3 + x)[ln(x + -5) + ln(x + 5)] = 0 Reorder the terms: ln(-3 + x)[ln(-5 + x) + ln(x + 5)] = 0 ln(-3 + x)[(-5 * ln + x * ln) + ln(x + 5)] = 0 ln(-3 + x)[(-5ln + lnx) + ln(x + 5)] = 0 Reorder the terms: ln(-3 + x)[-5ln + lnx + ln(5 + x)] = 0 ln(-3 + x)[-5ln + lnx + (5 * ln + x * ln)] = 0 ln(-3 + x)[-5ln + lnx + (5ln + lnx)] = 0 Reorder the terms: ln(-3 + x)[-5ln + 5ln + lnx + lnx] = 0 Combine like terms: -5ln + 5ln = 0 ln(-3 + x)[0 + lnx + lnx] = 0 ln(-3 + x)[lnx + lnx] = 0 Combine like terms: lnx + lnx = 2lnx ln(-3 + x)[2lnx] = 0 Remove brackets around [2lnx] ln(-3 + x) * 2lnx = 0 Reorder the terms for easier multiplication: 2ln * lnx(-3 + x) = 0 Multiply ln * lnx 2l2n2x(-3 + x) = 0 (-3 * 2l2n2x + x * 2l2n2x) = 0 (-6l2n2x + 2l2n2x2) = 0 Solving -6l2n2x + 2l2n2x2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2l2n2x'. 2l2n2x(-3 + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'l2n2x' equal to zero and attempt to solve: Simplifying l2n2x = 0 Solving l2n2x = 0 Move all terms containing l to the left, all other terms to the right. Simplifying l2n2x = 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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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