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Simplifying ln(x + -35) + ln(x + 180) = 3ln(6) Reorder the terms: ln(-35 + x) + ln(x + 180) = 3ln(6) (-35 * ln + x * ln) + ln(x + 180) = 3ln(6) (-35ln + lnx) + ln(x + 180) = 3ln(6) Reorder the terms: -35ln + lnx + ln(180 + x) = 3ln(6) -35ln + lnx + (180 * ln + x * ln) = 3ln(6) -35ln + lnx + (180ln + lnx) = 3ln(6) Reorder the terms: -35ln + 180ln + lnx + lnx = 3ln(6) Combine like terms: -35ln + 180ln = 145ln 145ln + lnx + lnx = 3ln(6) Combine like terms: lnx + lnx = 2lnx 145ln + 2lnx = 3ln(6) Reorder the terms for easier multiplication: 145ln + 2lnx = 3 * 6ln Multiply 3 * 6 145ln + 2lnx = 18ln Solving 145ln + 2lnx = 18ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18ln' to each side of the equation. 145ln + -18ln + 2lnx = 18ln + -18ln Combine like terms: 145ln + -18ln = 127ln 127ln + 2lnx = 18ln + -18ln Combine like terms: 18ln + -18ln = 0 127ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(127 + 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 '(127 + 2x)' equal to zero and attempt to solve: Simplifying 127 + 2x = 0 Solving 127 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-127' to each side of the equation. 127 + -127 + 2x = 0 + -127 Combine like terms: 127 + -127 = 0 0 + 2x = 0 + -127 2x = 0 + -127 Combine like terms: 0 + -127 = -127 2x = -127 Add '-2x' to each side of the equation. 2x + -2x = -127 + -2x Combine like terms: 2x + -2x = 0 0 = -127 + -2x Simplifying 0 = -127 + -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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