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