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Simplifying Ln(x + 6) + ln(3) = 2ln(x) Reorder the terms: nL(6 + x) + ln(3) = 2ln(x) (6 * nL + x * nL) + ln(3) = 2ln(x) (6nL + nxL) + ln(3) = 2ln(x) Reorder the terms for easier multiplication: 6nL + nxL + 3ln = 2ln(x) Reorder the terms: 3ln + 6nL + nxL = 2ln(x) Multiply ln * x 3ln + 6nL + nxL = 2lnx Solving 3ln + 6nL + nxL = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. 3ln + 6nL + -2lnx + nxL = 2lnx + -2lnx Reorder the terms: 3ln + -2lnx + 6nL + nxL = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 3ln + -2lnx + 6nL + nxL = 0 Add '-6nL' to each side of the equation. 3ln + -2lnx + 6nL + -6nL + nxL = 0 + -6nL Combine like terms: 6nL + -6nL = 0 3ln + -2lnx + 0 + nxL = 0 + -6nL 3ln + -2lnx + nxL = 0 + -6nL Remove the zero: 3ln + -2lnx + nxL = -6nL Add '-1nxL' to each side of the equation. 3ln + -2lnx + nxL + -1nxL = -6nL + -1nxL Combine like terms: nxL + -1nxL = 0 3ln + -2lnx + 0 = -6nL + -1nxL 3ln + -2lnx = -6nL + -1nxL Reorder the terms: 3ln + -2lnx + 6nL + nxL = -6nL + 6nL + -1nxL + nxL Combine like terms: -6nL + 6nL = 0 3ln + -2lnx + 6nL + nxL = 0 + -1nxL + nxL 3ln + -2lnx + 6nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 3ln + -2lnx + 6nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(3l + -2lx + 6L + xL) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(3l + -2lx + 6L + xL)' equal to zero and attempt to solve: Simplifying 3l + -2lx + 6L + xL = 0 Reorder the terms: 6L + 3l + -2lx + xL = 0 Solving 6L + 3l + -2lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-6L' to each side of the equation. 6L + 3l + -2lx + -6L + xL = 0 + -6L Reorder the terms: 6L + -6L + 3l + -2lx + xL = 0 + -6L Combine like terms: 6L + -6L = 0 0 + 3l + -2lx + xL = 0 + -6L 3l + -2lx + xL = 0 + -6L Remove the zero: 3l + -2lx + xL = -6L Add '-1xL' to each side of the equation. 3l + -2lx + xL + -1xL = -6L + -1xL Combine like terms: xL + -1xL = 0 3l + -2lx + 0 = -6L + -1xL 3l + -2lx = -6L + -1xL 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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