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Simplifying Ln(x + 5) + lnx = ln(14) Reorder the terms: nL(5 + x) + lnx = ln(14) (5 * nL + x * nL) + lnx = ln(14) (5nL + nxL) + lnx = ln(14) Reorder the terms: lnx + 5nL + nxL = ln(14) Reorder the terms for easier multiplication: lnx + 5nL + nxL = 14ln Solving lnx + 5nL + nxL = 14ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. lnx + 5nL + -14ln + nxL = 14ln + -14ln Reorder the terms: -14ln + lnx + 5nL + nxL = 14ln + -14ln Combine like terms: 14ln + -14ln = 0 -14ln + lnx + 5nL + nxL = 0 Add '-5nL' to each side of the equation. -14ln + lnx + 5nL + -5nL + nxL = 0 + -5nL Combine like terms: 5nL + -5nL = 0 -14ln + lnx + 0 + nxL = 0 + -5nL -14ln + lnx + nxL = 0 + -5nL Remove the zero: -14ln + lnx + nxL = -5nL Add '-1nxL' to each side of the equation. -14ln + lnx + nxL + -1nxL = -5nL + -1nxL Combine like terms: nxL + -1nxL = 0 -14ln + lnx + 0 = -5nL + -1nxL -14ln + lnx = -5nL + -1nxL Reorder the terms: -14ln + lnx + 5nL + nxL = -5nL + 5nL + -1nxL + nxL Combine like terms: -5nL + 5nL = 0 -14ln + lnx + 5nL + nxL = 0 + -1nxL + nxL -14ln + lnx + 5nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 -14ln + lnx + 5nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-14l + lx + 5L + 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 '(-14l + lx + 5L + xL)' equal to zero and attempt to solve: Simplifying -14l + lx + 5L + xL = 0 Reorder the terms: 5L + -14l + lx + xL = 0 Solving 5L + -14l + lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-5L' to each side of the equation. 5L + -14l + lx + -5L + xL = 0 + -5L Reorder the terms: 5L + -5L + -14l + lx + xL = 0 + -5L Combine like terms: 5L + -5L = 0 0 + -14l + lx + xL = 0 + -5L -14l + lx + xL = 0 + -5L Remove the zero: -14l + lx + xL = -5L Add '-1xL' to each side of the equation. -14l + lx + xL + -1xL = -5L + -1xL Combine like terms: xL + -1xL = 0 -14l + lx + 0 = -5L + -1xL -14l + lx = -5L + -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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