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Simplifying 8ln(x + 8) + -1ln(5) = ln(x) Reorder the terms: 8ln(8 + x) + -1ln(5) = ln(x) (8 * 8ln + x * 8ln) + -1ln(5) = ln(x) (64ln + 8lnx) + -1ln(5) = ln(x) Reorder the terms for easier multiplication: 64ln + 8lnx + -1 * 5ln = ln(x) Multiply -1 * 5 64ln + 8lnx + -5ln = ln(x) Reorder the terms: 64ln + -5ln + 8lnx = ln(x) Combine like terms: 64ln + -5ln = 59ln 59ln + 8lnx = ln(x) Multiply ln * x 59ln + 8lnx = lnx Solving 59ln + 8lnx = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. 59ln + 8lnx + -1lnx = lnx + -1lnx Combine like terms: 8lnx + -1lnx = 7lnx 59ln + 7lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 59ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(59 + 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 '(59 + 7x)' equal to zero and attempt to solve: Simplifying 59 + 7x = 0 Solving 59 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-59' to each side of the equation. 59 + -59 + 7x = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 7x = 0 + -59 7x = 0 + -59 Combine like terms: 0 + -59 = -59 7x = -59 Add '-7x' to each side of the equation. 7x + -7x = -59 + -7x Combine like terms: 7x + -7x = 0 0 = -59 + -7x Simplifying 0 = -59 + -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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