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Simplifying ln(x) + ln(x + -2) = ln(195) Multiply ln * x lnx + ln(x + -2) = ln(195) Reorder the terms: lnx + ln(-2 + x) = ln(195) lnx + (-2 * ln + x * ln) = ln(195) lnx + (-2ln + lnx) = ln(195) Reorder the terms: -2ln + lnx + lnx = ln(195) Combine like terms: lnx + lnx = 2lnx -2ln + 2lnx = ln(195) Reorder the terms for easier multiplication: -2ln + 2lnx = 195ln Solving -2ln + 2lnx = 195ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-195ln' to each side of the equation. -2ln + -195ln + 2lnx = 195ln + -195ln Combine like terms: -2ln + -195ln = -197ln -197ln + 2lnx = 195ln + -195ln Combine like terms: 195ln + -195ln = 0 -197ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-197 + 2x) = 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 '(-197 + 2x)' equal to zero and attempt to solve: Simplifying -197 + 2x = 0 Solving -197 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '197' to each side of the equation. -197 + 197 + 2x = 0 + 197 Combine like terms: -197 + 197 = 0 0 + 2x = 0 + 197 2x = 0 + 197 Combine like terms: 0 + 197 = 197 2x = 197 Add '-2x' to each side of the equation. 2x + -2x = 197 + -2x Combine like terms: 2x + -2x = 0 0 = 197 + -2x Simplifying 0 = 197 + -2x 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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