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Simplifying ln(2x) + ln(x + -3) = ln(4) Remove parenthesis around (2x) ln * 2x + ln(x + -3) = ln(4) Reorder the terms for easier multiplication: 2ln * x + ln(x + -3) = ln(4) Multiply ln * x 2lnx + ln(x + -3) = ln(4) Reorder the terms: 2lnx + ln(-3 + x) = ln(4) 2lnx + (-3 * ln + x * ln) = ln(4) 2lnx + (-3ln + lnx) = ln(4) Reorder the terms: -3ln + 2lnx + lnx = ln(4) Combine like terms: 2lnx + lnx = 3lnx -3ln + 3lnx = ln(4) Reorder the terms for easier multiplication: -3ln + 3lnx = 4ln Solving -3ln + 3lnx = 4ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. -3ln + -4ln + 3lnx = 4ln + -4ln Combine like terms: -3ln + -4ln = -7ln -7ln + 3lnx = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 -7ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-7 + 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 '(-7 + 3x)' equal to zero and attempt to solve: Simplifying -7 + 3x = 0 Solving -7 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3x = 0 + 7 3x = 0 + 7 Combine like terms: 0 + 7 = 7 3x = 7 Add '-3x' to each side of the equation. 3x + -3x = 7 + -3x Combine like terms: 3x + -3x = 0 0 = 7 + -3x Simplifying 0 = 7 + -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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