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Simplifying Ln(x) + ln(x + 1) = ln(6) Multiply nL * x nxL + ln(x + 1) = ln(6) Reorder the terms: nxL + ln(1 + x) = ln(6) nxL + (1 * ln + x * ln) = ln(6) nxL + (1ln + lnx) = ln(6) Reorder the terms: 1ln + lnx + nxL = ln(6) Reorder the terms for easier multiplication: 1ln + lnx + nxL = 6ln Solving 1ln + lnx + nxL = 6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 1ln + lnx + -6ln + nxL = 6ln + -6ln Reorder the terms: 1ln + -6ln + lnx + nxL = 6ln + -6ln Combine like terms: 1ln + -6ln = -5ln -5ln + lnx + nxL = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 -5ln + lnx + nxL = 0 Add '-1nxL' to each side of the equation. -5ln + lnx + nxL + -1nxL = 0 + -1nxL Combine like terms: nxL + -1nxL = 0 -5ln + lnx + 0 = 0 + -1nxL -5ln + lnx = 0 + -1nxL Remove the zero: -5ln + lnx = -1nxL Combine like terms: -1nxL + nxL = 0 -5ln + lnx + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-5l + lx + 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 '(-5l + lx + xL)' equal to zero and attempt to solve: Simplifying -5l + lx + xL = 0 Solving -5l + lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-1xL' to each side of the equation. -5l + lx + xL + -1xL = 0 + -1xL Combine like terms: xL + -1xL = 0 -5l + lx + 0 = 0 + -1xL -5l + lx = 0 + -1xL Remove the zero: -5l + lx = -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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