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Simplifying ln(8x + -3) + -1lnx = ln(7) Reorder the terms: ln(-3 + 8x) + -1lnx = ln(7) (-3 * ln + 8x * ln) + -1lnx = ln(7) (-3ln + 8lnx) + -1lnx = ln(7) Combine like terms: 8lnx + -1lnx = 7lnx -3ln + 7lnx = ln(7) Reorder the terms for easier multiplication: -3ln + 7lnx = 7ln Solving -3ln + 7lnx = 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. -3ln + -7ln + 7lnx = 7ln + -7ln Combine like terms: -3ln + -7ln = -10ln -10ln + 7lnx = 7ln + -7ln Combine like terms: 7ln + -7ln = 0 -10ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + 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 '(-10 + 7x)' equal to zero and attempt to solve: Simplifying -10 + 7x = 0 Solving -10 + 7x = 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 + 7x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 7x = 0 + 10 7x = 0 + 10 Combine like terms: 0 + 10 = 10 7x = 10 Add '-7x' to each side of the equation. 7x + -7x = 10 + -7x Combine like terms: 7x + -7x = 0 0 = 10 + -7x Simplifying 0 = 10 + -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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