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Simplifying ln(14x + 6) = ln(10) Reorder the terms: ln(6 + 14x) = ln(10) (6 * ln + 14x * ln) = ln(10) (6ln + 14lnx) = ln(10) Reorder the terms for easier multiplication: 6ln + 14lnx = 10ln Solving 6ln + 14lnx = 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. 6ln + -10ln + 14lnx = 10ln + -10ln Combine like terms: 6ln + -10ln = -4ln -4ln + 14lnx = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -4ln + 14lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-2 + 7x) = 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 '(-2 + 7x)' equal to zero and attempt to solve: Simplifying -2 + 7x = 0 Solving -2 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 7x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7x = 0 + 2 7x = 0 + 2 Combine like terms: 0 + 2 = 2 7x = 2 Add '-7x' to each side of the equation. 7x + -7x = 2 + -7x Combine like terms: 7x + -7x = 0 0 = 2 + -7x Simplifying 0 = 2 + -7x 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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