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Simplifying ln(6x) + 8ln(x) = ln(7) Remove parenthesis around (6x) ln * 6x + 8ln(x) = ln(7) Reorder the terms for easier multiplication: 6ln * x + 8ln(x) = ln(7) Multiply ln * x 6lnx + 8ln(x) = ln(7) Multiply ln * x 6lnx + 8lnx = ln(7) Combine like terms: 6lnx + 8lnx = 14lnx 14lnx = ln(7) Reorder the terms for easier multiplication: 14lnx = 7ln Solving 14lnx = 7ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. -7ln + 14lnx = 7ln + -7ln Combine like terms: 7ln + -7ln = 0 -7ln + 14lnx = 0 Factor out the Greatest Common Factor (GCF), '7ln'. 7ln(-1 + 2x) = 0 Ignore the factor 7.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 '(-1 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Add '-2x' to each side of the equation. 2x + -2x = 1 + -2x Combine like terms: 2x + -2x = 0 0 = 1 + -2x Simplifying 0 = 1 + -2x 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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