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Simplifying Ln(x) + ln(x + 12) = ln(8x + 32) Multiply nL * x nxL + ln(x + 12) = ln(8x + 32) Reorder the terms: nxL + ln(12 + x) = ln(8x + 32) nxL + (12 * ln + x * ln) = ln(8x + 32) nxL + (12ln + lnx) = ln(8x + 32) Reorder the terms: 12ln + lnx + nxL = ln(8x + 32) Reorder the terms: 12ln + lnx + nxL = ln(32 + 8x) 12ln + lnx + nxL = (32 * ln + 8x * ln) 12ln + lnx + nxL = (32ln + 8lnx) Solving 12ln + lnx + nxL = 32ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-32ln' to each side of the equation. 12ln + lnx + -32ln + nxL = 32ln + -32ln + 8lnx Reorder the terms: 12ln + -32ln + lnx + nxL = 32ln + -32ln + 8lnx Combine like terms: 12ln + -32ln = -20ln -20ln + lnx + nxL = 32ln + -32ln + 8lnx Combine like terms: 32ln + -32ln = 0 -20ln + lnx + nxL = 0 + 8lnx -20ln + lnx + nxL = 8lnx Add '-8lnx' to each side of the equation. -20ln + lnx + -8lnx + nxL = 8lnx + -8lnx Combine like terms: lnx + -8lnx = -7lnx -20ln + -7lnx + nxL = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 -20ln + -7lnx + nxL = 0 Add '-1nxL' to each side of the equation. -20ln + -7lnx + nxL + -1nxL = 0 + -1nxL Combine like terms: nxL + -1nxL = 0 -20ln + -7lnx + 0 = 0 + -1nxL -20ln + -7lnx = 0 + -1nxL Remove the zero: -20ln + -7lnx = -1nxL Combine like terms: -1nxL + nxL = 0 -20ln + -7lnx + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-20l + -7lx + 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 '(-20l + -7lx + xL)' equal to zero and attempt to solve: Simplifying -20l + -7lx + xL = 0 Solving -20l + -7lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-1xL' to each side of the equation. -20l + -7lx + xL + -1xL = 0 + -1xL Combine like terms: xL + -1xL = 0 -20l + -7lx + 0 = 0 + -1xL -20l + -7lx = 0 + -1xL Remove the zero: -20l + -7lx = -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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