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Simplifying ln(6x) + ln(9x) = ln(55) Remove parenthesis around (6x) ln * 6x + ln(9x) = ln(55) Reorder the terms for easier multiplication: 6ln * x + ln(9x) = ln(55) Multiply ln * x 6lnx + ln(9x) = ln(55) Remove parenthesis around (9x) 6lnx + ln * 9x = ln(55) Reorder the terms for easier multiplication: 6lnx + 9ln * x = ln(55) Multiply ln * x 6lnx + 9lnx = ln(55) Combine like terms: 6lnx + 9lnx = 15lnx 15lnx = ln(55) Reorder the terms for easier multiplication: 15lnx = 55ln Solving 15lnx = 55ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-55ln' to each side of the equation. -55ln + 15lnx = 55ln + -55ln Combine like terms: 55ln + -55ln = 0 -55ln + 15lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(-11 + 3x) = 0 Ignore the factor 5.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 '(-11 + 3x)' equal to zero and attempt to solve: Simplifying -11 + 3x = 0 Solving -11 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 3x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 3x = 0 + 11 3x = 0 + 11 Combine like terms: 0 + 11 = 11 3x = 11 Add '-3x' to each side of the equation. 3x + -3x = 11 + -3x Combine like terms: 3x + -3x = 0 0 = 11 + -3x Simplifying 0 = 11 + -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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