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Simplifying ln(7x) = ln(40 + -1x) Remove parenthesis around (7x) ln * 7x = ln(40 + -1x) Reorder the terms for easier multiplication: 7ln * x = ln(40 + -1x) Multiply ln * x 7lnx = ln(40 + -1x) 7lnx = (40 * ln + -1x * ln) 7lnx = (40ln + -1lnx) Solving 7lnx = 40ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-40ln' to each side of the equation. -40ln + 7lnx = 40ln + -40ln + -1lnx Combine like terms: 40ln + -40ln = 0 -40ln + 7lnx = 0 + -1lnx -40ln + 7lnx = -1lnx Add 'lnx' to each side of the equation. -40ln + 7lnx + lnx = -1lnx + lnx Combine like terms: 7lnx + lnx = 8lnx -40ln + 8lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -40ln + 8lnx = 0 Factor out the Greatest Common Factor (GCF), '8ln'. 8ln(-5 + x) = 0 Ignore the factor 8.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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -1x 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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