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