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Simplifying ln(2x) + ln(x + 2) = ln(30) Remove parenthesis around (2x) ln * 2x + ln(x + 2) = ln(30) Reorder the terms for easier multiplication: 2ln * x + ln(x + 2) = ln(30) Multiply ln * x 2lnx + ln(x + 2) = ln(30) Reorder the terms: 2lnx + ln(2 + x) = ln(30) 2lnx + (2 * ln + x * ln) = ln(30) 2lnx + (2ln + lnx) = ln(30) Reorder the terms: 2ln + 2lnx + lnx = ln(30) Combine like terms: 2lnx + lnx = 3lnx 2ln + 3lnx = ln(30) Reorder the terms for easier multiplication: 2ln + 3lnx = 30ln Solving 2ln + 3lnx = 30ln 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. 2ln + -30ln + 3lnx = 30ln + -30ln Combine like terms: 2ln + -30ln = -28ln -28ln + 3lnx = 30ln + -30ln Combine like terms: 30ln + -30ln = 0 -28ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-28 + 3x) = 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 '(-28 + 3x)' equal to zero and attempt to solve: Simplifying -28 + 3x = 0 Solving -28 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + 3x = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 3x = 0 + 28 3x = 0 + 28 Combine like terms: 0 + 28 = 28 3x = 28 Add '-3x' to each side of the equation. 3x + -3x = 28 + -3x Combine like terms: 3x + -3x = 0 0 = 28 + -3x Simplifying 0 = 28 + -3x 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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