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Simplifying ln(x2) + ln(2x) = ln(x + 30) Multiply ln * x2 lnx2 + ln(2x) = ln(x + 30) Remove parenthesis around (2x) lnx2 + ln * 2x = ln(x + 30) Reorder the terms for easier multiplication: lnx2 + 2ln * x = ln(x + 30) Multiply ln * x lnx2 + 2lnx = ln(x + 30) Reorder the terms: 2lnx + lnx2 = ln(x + 30) Reorder the terms: 2lnx + lnx2 = ln(30 + x) 2lnx + lnx2 = (30 * ln + x * ln) 2lnx + lnx2 = (30ln + lnx) Solving 2lnx + lnx2 = 30ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-30ln' to each side of the equation. 2lnx + -30ln + lnx2 = 30ln + -30ln + lnx Reorder the terms: -30ln + 2lnx + lnx2 = 30ln + -30ln + lnx Combine like terms: 30ln + -30ln = 0 -30ln + 2lnx + lnx2 = 0 + lnx -30ln + 2lnx + lnx2 = lnx Add '-1lnx' to each side of the equation. -30ln + 2lnx + -1lnx + lnx2 = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -30ln + 1lnx + lnx2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -30ln + 1lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-30 + x + x2) = 0 Factor a trinomial. ln((-6 + -1x)(5 + -1x)) = 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 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 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 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Add 'x' to each side of the equation. -1x + x = 6 + x Combine like terms: -1x + x = 0 0 = 6 + x Simplifying 0 = 6 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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