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Simplifying ln(x + 2) + ln(2x + 2) = ln(40) Reorder the terms: ln(2 + x) + ln(2x + 2) = ln(40) (2 * ln + x * ln) + ln(2x + 2) = ln(40) (2ln + lnx) + ln(2x + 2) = ln(40) Reorder the terms: 2ln + lnx + ln(2 + 2x) = ln(40) 2ln + lnx + (2 * ln + 2x * ln) = ln(40) 2ln + lnx + (2ln + 2lnx) = ln(40) Reorder the terms: 2ln + 2ln + lnx + 2lnx = ln(40) Combine like terms: 2ln + 2ln = 4ln 4ln + lnx + 2lnx = ln(40) Combine like terms: lnx + 2lnx = 3lnx 4ln + 3lnx = ln(40) Reorder the terms for easier multiplication: 4ln + 3lnx = 40ln Solving 4ln + 3lnx = 40ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-40ln' to each side of the equation. 4ln + -40ln + 3lnx = 40ln + -40ln Combine like terms: 4ln + -40ln = -36ln -36ln + 3lnx = 40ln + -40ln Combine like terms: 40ln + -40ln = 0 -36ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-12 + x) = 0 Ignore the factor 3.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 '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Add '-1x' to each side of the equation. x + -1x = 12 + -1x Combine like terms: x + -1x = 0 0 = 12 + -1x Simplifying 0 = 12 + -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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