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Simplifying ln(6x) + -1ln(3) = ln(27) Remove parenthesis around (6x) ln * 6x + -1ln(3) = ln(27) Reorder the terms for easier multiplication: 6ln * x + -1ln(3) = ln(27) Multiply ln * x 6lnx + -1ln(3) = ln(27) Reorder the terms for easier multiplication: 6lnx + -1 * 3ln = ln(27) Multiply -1 * 3 6lnx + -3ln = ln(27) Reorder the terms: -3ln + 6lnx = ln(27) Reorder the terms for easier multiplication: -3ln + 6lnx = 27ln Solving -3ln + 6lnx = 27ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-27ln' to each side of the equation. -3ln + -27ln + 6lnx = 27ln + -27ln Combine like terms: -3ln + -27ln = -30ln -30ln + 6lnx = 27ln + -27ln Combine like terms: 27ln + -27ln = 0 -30ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '6ln'. 6ln(-5 + x) = 0 Ignore the factor 6.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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -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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