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Simplifying Ln(x) + ln(2x + -3) = ln(9) Multiply nL * x nxL + ln(2x + -3) = ln(9) Reorder the terms: nxL + ln(-3 + 2x) = ln(9) nxL + (-3 * ln + 2x * ln) = ln(9) nxL + (-3ln + 2lnx) = ln(9) Reorder the terms: -3ln + 2lnx + nxL = ln(9) Reorder the terms for easier multiplication: -3ln + 2lnx + nxL = 9ln Solving -3ln + 2lnx + nxL = 9ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. -3ln + 2lnx + -9ln + nxL = 9ln + -9ln Reorder the terms: -3ln + -9ln + 2lnx + nxL = 9ln + -9ln Combine like terms: -3ln + -9ln = -12ln -12ln + 2lnx + nxL = 9ln + -9ln Combine like terms: 9ln + -9ln = 0 -12ln + 2lnx + nxL = 0 Add '-1nxL' to each side of the equation. -12ln + 2lnx + nxL + -1nxL = 0 + -1nxL Combine like terms: nxL + -1nxL = 0 -12ln + 2lnx + 0 = 0 + -1nxL -12ln + 2lnx = 0 + -1nxL Remove the zero: -12ln + 2lnx = -1nxL Combine like terms: -1nxL + nxL = 0 -12ln + 2lnx + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-12l + 2lx + 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 '(-12l + 2lx + xL)' equal to zero and attempt to solve: Simplifying -12l + 2lx + xL = 0 Solving -12l + 2lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-1xL' to each side of the equation. -12l + 2lx + xL + -1xL = 0 + -1xL Combine like terms: xL + -1xL = 0 -12l + 2lx + 0 = 0 + -1xL -12l + 2lx = 0 + -1xL Remove the zero: -12l + 2lx = -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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