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