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Simplifying ln(x) + ln(x + -3) = ln(108) Multiply ln * x lnx + ln(x + -3) = ln(108) Reorder the terms: lnx + ln(-3 + x) = ln(108) lnx + (-3 * ln + x * ln) = ln(108) lnx + (-3ln + lnx) = ln(108) Reorder the terms: -3ln + lnx + lnx = ln(108) Combine like terms: lnx + lnx = 2lnx -3ln + 2lnx = ln(108) Reorder the terms for easier multiplication: -3ln + 2lnx = 108ln Solving -3ln + 2lnx = 108ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-108ln' to each side of the equation. -3ln + -108ln + 2lnx = 108ln + -108ln Combine like terms: -3ln + -108ln = -111ln -111ln + 2lnx = 108ln + -108ln Combine like terms: 108ln + -108ln = 0 -111ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-111 + 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 '(-111 + 2x)' equal to zero and attempt to solve: Simplifying -111 + 2x = 0 Solving -111 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '111' to each side of the equation. -111 + 111 + 2x = 0 + 111 Combine like terms: -111 + 111 = 0 0 + 2x = 0 + 111 2x = 0 + 111 Combine like terms: 0 + 111 = 111 2x = 111 Add '-2x' to each side of the equation. 2x + -2x = 111 + -2x Combine like terms: 2x + -2x = 0 0 = 111 + -2x Simplifying 0 = 111 + -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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