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Simplifying ln(7x) + ln(3x) = ln(22) Remove parenthesis around (7x) ln * 7x + ln(3x) = ln(22) Reorder the terms for easier multiplication: 7ln * x + ln(3x) = ln(22) Multiply ln * x 7lnx + ln(3x) = ln(22) Remove parenthesis around (3x) 7lnx + ln * 3x = ln(22) Reorder the terms for easier multiplication: 7lnx + 3ln * x = ln(22) Multiply ln * x 7lnx + 3lnx = ln(22) Combine like terms: 7lnx + 3lnx = 10lnx 10lnx = ln(22) Reorder the terms for easier multiplication: 10lnx = 22ln Solving 10lnx = 22ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-22ln' to each side of the equation. -22ln + 10lnx = 22ln + -22ln Combine like terms: 22ln + -22ln = 0 -22ln + 10lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-11 + 5x) = 0 Ignore the factor 2.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 + 5x)' equal to zero and attempt to solve: Simplifying -11 + 5x = 0 Solving -11 + 5x = 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 + 5x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 5x = 0 + 11 5x = 0 + 11 Combine like terms: 0 + 11 = 11 5x = 11 Add '-5x' to each side of the equation. 5x + -5x = 11 + -5x Combine like terms: 5x + -5x = 0 0 = 11 + -5x Simplifying 0 = 11 + -5x 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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