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Simplifying Ln(3x + -1) + ln(2x + 3) = ln * 10 Reorder the terms: nL(-1 + 3x) + ln(2x + 3) = ln * 10 (-1 * nL + 3x * nL) + ln(2x + 3) = ln * 10 (-1nL + 3nxL) + ln(2x + 3) = ln * 10 Reorder the terms: -1nL + 3nxL + ln(3 + 2x) = ln * 10 -1nL + 3nxL + (3 * ln + 2x * ln) = ln * 10 -1nL + 3nxL + (3ln + 2lnx) = ln * 10 Reorder the terms: 3ln + 2lnx + -1nL + 3nxL = ln * 10 Reorder the terms for easier multiplication: 3ln + 2lnx + -1nL + 3nxL = 10ln Solving 3ln + 2lnx + -1nL + 3nxL = 10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. 3ln + 2lnx + -1nL + -10ln + 3nxL = 10ln + -10ln Reorder the terms: 3ln + -10ln + 2lnx + -1nL + 3nxL = 10ln + -10ln Combine like terms: 3ln + -10ln = -7ln -7ln + 2lnx + -1nL + 3nxL = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -7ln + 2lnx + -1nL + 3nxL = 0 Add 'nL' to each side of the equation. -7ln + 2lnx + -1nL + nL + 3nxL = 0 + nL Combine like terms: -1nL + nL = 0 -7ln + 2lnx + 0 + 3nxL = 0 + nL -7ln + 2lnx + 3nxL = 0 + nL Remove the zero: -7ln + 2lnx + 3nxL = nL Add '-3nxL' to each side of the equation. -7ln + 2lnx + 3nxL + -3nxL = nL + -3nxL Combine like terms: 3nxL + -3nxL = 0 -7ln + 2lnx + 0 = nL + -3nxL -7ln + 2lnx = nL + -3nxL Reorder the terms: -7ln + 2lnx + -1nL + 3nxL = nL + -1nL + -3nxL + 3nxL Combine like terms: nL + -1nL = 0 -7ln + 2lnx + -1nL + 3nxL = 0 + -3nxL + 3nxL -7ln + 2lnx + -1nL + 3nxL = -3nxL + 3nxL Combine like terms: -3nxL + 3nxL = 0 -7ln + 2lnx + -1nL + 3nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-7l + 2lx + -1L + 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 + 2lx + -1L + 3xL)' equal to zero and attempt to solve: Simplifying -7l + 2lx + -1L + 3xL = 0 Reorder the terms: -1L + -7l + 2lx + 3xL = 0 Solving -1L + -7l + 2lx + 3xL = 0 Move all terms containing l to the left, all other terms to the right. Add 'L' to each side of the equation. -1L + -7l + 2lx + L + 3xL = 0 + L Reorder the terms: -1L + L + -7l + 2lx + 3xL = 0 + L Combine like terms: -1L + L = 0 0 + -7l + 2lx + 3xL = 0 + L -7l + 2lx + 3xL = 0 + L Remove the zero: -7l + 2lx + 3xL = L Add '-3xL' to each side of the equation. -7l + 2lx + 3xL + -3xL = L + -3xL Combine like terms: 3xL + -3xL = 0 -7l + 2lx + 0 = L + -3xL -7l + 2lx = L + -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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