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Simplifying Ln(3x) + ln(x + -1) = ln(6) Remove parenthesis around (3x) nL * 3x + ln(x + -1) = ln(6) Reorder the terms for easier multiplication: 3nL * x + ln(x + -1) = ln(6) Multiply nL * x 3nxL + ln(x + -1) = ln(6) Reorder the terms: 3nxL + ln(-1 + x) = ln(6) 3nxL + (-1 * ln + x * ln) = ln(6) 3nxL + (-1ln + lnx) = ln(6) Reorder the terms: -1ln + lnx + 3nxL = ln(6) Reorder the terms for easier multiplication: -1ln + lnx + 3nxL = 6ln Solving -1ln + lnx + 3nxL = 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 + 3nxL = 6ln + -6ln Reorder the terms: -1ln + -6ln + lnx + 3nxL = 6ln + -6ln Combine like terms: -1ln + -6ln = -7ln -7ln + lnx + 3nxL = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 -7ln + lnx + 3nxL = 0 Add '-3nxL' to each side of the equation. -7ln + lnx + 3nxL + -3nxL = 0 + -3nxL Combine like terms: 3nxL + -3nxL = 0 -7ln + lnx + 0 = 0 + -3nxL -7ln + lnx = 0 + -3nxL Remove the zero: -7ln + lnx = -3nxL Combine like terms: -3nxL + 3nxL = 0 -7ln + lnx + 3nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-7l + lx + 3xL) = 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 '(-7l + lx + 3xL)' equal to zero and attempt to solve: Simplifying -7l + lx + 3xL = 0 Solving -7l + lx + 3xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-3xL' to each side of the equation. -7l + lx + 3xL + -3xL = 0 + -3xL Combine like terms: 3xL + -3xL = 0 -7l + lx + 0 = 0 + -3xL -7l + lx = 0 + -3xL Remove the zero: -7l + lx = -3xL 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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