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Simplifying ln(8x + -4) = ln(2) + ln(x) Reorder the terms: ln(-4 + 8x) = ln(2) + ln(x) (-4 * ln + 8x * ln) = ln(2) + ln(x) (-4ln + 8lnx) = ln(2) + ln(x) Reorder the terms for easier multiplication: -4ln + 8lnx = 2ln + ln(x) Multiply ln * x -4ln + 8lnx = 2ln + lnx Solving -4ln + 8lnx = 2ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. -4ln + -2ln + 8lnx = 2ln + -2ln + lnx Combine like terms: -4ln + -2ln = -6ln -6ln + 8lnx = 2ln + -2ln + lnx Combine like terms: 2ln + -2ln = 0 -6ln + 8lnx = 0 + lnx -6ln + 8lnx = lnx Add '-1lnx' to each side of the equation. -6ln + 8lnx + -1lnx = lnx + -1lnx Combine like terms: 8lnx + -1lnx = 7lnx -6ln + 7lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -6ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-6 + 7x) = 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 '(-6 + 7x)' equal to zero and attempt to solve: Simplifying -6 + 7x = 0 Solving -6 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 7x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 7x = 0 + 6 7x = 0 + 6 Combine like terms: 0 + 6 = 6 7x = 6 Add '-7x' to each side of the equation. 7x + -7x = 6 + -7x Combine like terms: 7x + -7x = 0 0 = 6 + -7x Simplifying 0 = 6 + -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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