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Simplifying Ln(x3 + 10x2) + -1ln(x) = ln(24) Reorder the terms: nL(10x2 + x3) + -1ln(x) = ln(24) (10x2 * nL + x3 * nL) + -1ln(x) = ln(24) (10nx2L + nx3L) + -1ln(x) = ln(24) Multiply ln * x 10nx2L + nx3L + -1lnx = ln(24) Reorder the terms: -1lnx + 10nx2L + nx3L = ln(24) Reorder the terms for easier multiplication: -1lnx + 10nx2L + nx3L = 24ln Solving -1lnx + 10nx2L + nx3L = 24ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. -1lnx + 10nx2L + -24ln + nx3L = 24ln + -24ln Reorder the terms: -24ln + -1lnx + 10nx2L + nx3L = 24ln + -24ln Combine like terms: 24ln + -24ln = 0 -24ln + -1lnx + 10nx2L + nx3L = 0 Add '-10nx2L' to each side of the equation. -24ln + -1lnx + 10nx2L + -10nx2L + nx3L = 0 + -10nx2L Combine like terms: 10nx2L + -10nx2L = 0 -24ln + -1lnx + 0 + nx3L = 0 + -10nx2L -24ln + -1lnx + nx3L = 0 + -10nx2L Remove the zero: -24ln + -1lnx + nx3L = -10nx2L Add '-1nx3L' to each side of the equation. -24ln + -1lnx + nx3L + -1nx3L = -10nx2L + -1nx3L Combine like terms: nx3L + -1nx3L = 0 -24ln + -1lnx + 0 = -10nx2L + -1nx3L -24ln + -1lnx = -10nx2L + -1nx3L Reorder the terms: -24ln + -1lnx + 10nx2L + nx3L = -10nx2L + 10nx2L + -1nx3L + nx3L Combine like terms: -10nx2L + 10nx2L = 0 -24ln + -1lnx + 10nx2L + nx3L = 0 + -1nx3L + nx3L -24ln + -1lnx + 10nx2L + nx3L = -1nx3L + nx3L Combine like terms: -1nx3L + nx3L = 0 -24ln + -1lnx + 10nx2L + nx3L = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-24l + -1lx + 10x2L + x3L) = 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 '(-24l + -1lx + 10x2L + x3L)' equal to zero and attempt to solve: Simplifying -24l + -1lx + 10x2L + x3L = 0 Solving -24l + -1lx + 10x2L + x3L = 0 Move all terms containing l to the left, all other terms to the right. Add '-10x2L' to each side of the equation. -24l + -1lx + 10x2L + -10x2L + x3L = 0 + -10x2L Combine like terms: 10x2L + -10x2L = 0 -24l + -1lx + 0 + x3L = 0 + -10x2L -24l + -1lx + x3L = 0 + -10x2L Remove the zero: -24l + -1lx + x3L = -10x2L Add '-1x3L' to each side of the equation. -24l + -1lx + x3L + -1x3L = -10x2L + -1x3L Combine like terms: x3L + -1x3L = 0 -24l + -1lx + 0 = -10x2L + -1x3L -24l + -1lx = -10x2L + -1x3L 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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