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Simplifying ln(x) + ln(x + -4) = ln(32) Multiply ln * x lnx + ln(x + -4) = ln(32) Reorder the terms: lnx + ln(-4 + x) = ln(32) lnx + (-4 * ln + x * ln) = ln(32) lnx + (-4ln + lnx) = ln(32) Reorder the terms: -4ln + lnx + lnx = ln(32) Combine like terms: lnx + lnx = 2lnx -4ln + 2lnx = ln(32) Reorder the terms for easier multiplication: -4ln + 2lnx = 32ln Solving -4ln + 2lnx = 32ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-32ln' to each side of the equation. -4ln + -32ln + 2lnx = 32ln + -32ln Combine like terms: -4ln + -32ln = -36ln -36ln + 2lnx = 32ln + -32ln Combine like terms: 32ln + -32ln = 0 -36ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-18 + x) = 0 Ignore the factor 2.Subproblem 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 '(-18 + x)' equal to zero and attempt to solve: Simplifying -18 + x = 0 Solving -18 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 0 + 18 Combine like terms: -18 + 18 = 0 0 + x = 0 + 18 x = 0 + 18 Combine like terms: 0 + 18 = 18 x = 18 Add '-1x' to each side of the equation. x + -1x = 18 + -1x Combine like terms: x + -1x = 0 0 = 18 + -1x Simplifying 0 = 18 + -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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