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Simplifying ln(3x) + ln(9x) = ln(28) Remove parenthesis around (3x) ln * 3x + ln(9x) = ln(28) Reorder the terms for easier multiplication: 3ln * x + ln(9x) = ln(28) Multiply ln * x 3lnx + ln(9x) = ln(28) Remove parenthesis around (9x) 3lnx + ln * 9x = ln(28) Reorder the terms for easier multiplication: 3lnx + 9ln * x = ln(28) Multiply ln * x 3lnx + 9lnx = ln(28) Combine like terms: 3lnx + 9lnx = 12lnx 12lnx = ln(28) Reorder the terms for easier multiplication: 12lnx = 28ln Solving 12lnx = 28ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-28ln' to each side of the equation. -28ln + 12lnx = 28ln + -28ln Combine like terms: 28ln + -28ln = 0 -28ln + 12lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(-7 + 3x) = 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 '(-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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