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Simplifying Ln(9x + 6) = ln(5x + -30) Reorder the terms: nL(6 + 9x) = ln(5x + -30) (6 * nL + 9x * nL) = ln(5x + -30) (6nL + 9nxL) = ln(5x + -30) Reorder the terms: 6nL + 9nxL = ln(-30 + 5x) 6nL + 9nxL = (-30 * ln + 5x * ln) 6nL + 9nxL = (-30ln + 5lnx) Solving 6nL + 9nxL = -30ln + 5lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '30ln' to each side of the equation. 6nL + 30ln + 9nxL = -30ln + 30ln + 5lnx Reorder the terms: 30ln + 6nL + 9nxL = -30ln + 30ln + 5lnx Combine like terms: -30ln + 30ln = 0 30ln + 6nL + 9nxL = 0 + 5lnx 30ln + 6nL + 9nxL = 5lnx Add '-5lnx' to each side of the equation. 30ln + 6nL + -5lnx + 9nxL = 5lnx + -5lnx Reorder the terms: 30ln + -5lnx + 6nL + 9nxL = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 30ln + -5lnx + 6nL + 9nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(30l + -5lx + 6L + 9xL) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(30l + -5lx + 6L + 9xL)' equal to zero and attempt to solve: Simplifying 30l + -5lx + 6L + 9xL = 0 Reorder the terms: 6L + 30l + -5lx + 9xL = 0 Solving 6L + 30l + -5lx + 9xL = 0 Move all terms containing n to the left, all other terms to the right. Add '-6L' to each side of the equation. 6L + 30l + -5lx + -6L + 9xL = 0 + -6L Reorder the terms: 6L + -6L + 30l + -5lx + 9xL = 0 + -6L Combine like terms: 6L + -6L = 0 0 + 30l + -5lx + 9xL = 0 + -6L 30l + -5lx + 9xL = 0 + -6L Remove the zero: 30l + -5lx + 9xL = -6L Add '-30l' to each side of the equation. 30l + -5lx + -30l + 9xL = -6L + -30l Reorder the terms: 30l + -30l + -5lx + 9xL = -6L + -30l Combine like terms: 30l + -30l = 0 0 + -5lx + 9xL = -6L + -30l -5lx + 9xL = -6L + -30l Add '5lx' to each side of the equation. -5lx + 5lx + 9xL = -6L + -30l + 5lx Combine like terms: -5lx + 5lx = 0 0 + 9xL = -6L + -30l + 5lx 9xL = -6L + -30l + 5lx Add '-9xL' to each side of the equation. 9xL + -9xL = -6L + -30l + 5lx + -9xL Combine like terms: 9xL + -9xL = 0 0 = -6L + -30l + 5lx + -9xL Simplifying 0 = -6L + -30l + 5lx + -9xL The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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