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Simplifying Ln(x + 7) + ln(x + -7) = ln(15) Reorder the terms: nL(7 + x) + ln(x + -7) = ln(15) (7 * nL + x * nL) + ln(x + -7) = ln(15) (7nL + nxL) + ln(x + -7) = ln(15) Reorder the terms: 7nL + nxL + ln(-7 + x) = ln(15) 7nL + nxL + (-7 * ln + x * ln) = ln(15) 7nL + nxL + (-7ln + lnx) = ln(15) Reorder the terms: -7ln + lnx + 7nL + nxL = ln(15) Reorder the terms for easier multiplication: -7ln + lnx + 7nL + nxL = 15ln Solving -7ln + lnx + 7nL + nxL = 15ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. -7ln + lnx + 7nL + -15ln + nxL = 15ln + -15ln Reorder the terms: -7ln + -15ln + lnx + 7nL + nxL = 15ln + -15ln Combine like terms: -7ln + -15ln = -22ln -22ln + lnx + 7nL + nxL = 15ln + -15ln Combine like terms: 15ln + -15ln = 0 -22ln + lnx + 7nL + nxL = 0 Add '-7nL' to each side of the equation. -22ln + lnx + 7nL + -7nL + nxL = 0 + -7nL Combine like terms: 7nL + -7nL = 0 -22ln + lnx + 0 + nxL = 0 + -7nL -22ln + lnx + nxL = 0 + -7nL Remove the zero: -22ln + lnx + nxL = -7nL Add '-1nxL' to each side of the equation. -22ln + lnx + nxL + -1nxL = -7nL + -1nxL Combine like terms: nxL + -1nxL = 0 -22ln + lnx + 0 = -7nL + -1nxL -22ln + lnx = -7nL + -1nxL Reorder the terms: -22ln + lnx + 7nL + nxL = -7nL + 7nL + -1nxL + nxL Combine like terms: -7nL + 7nL = 0 -22ln + lnx + 7nL + nxL = 0 + -1nxL + nxL -22ln + lnx + 7nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 -22ln + lnx + 7nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-22l + lx + 7L + 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 '(-22l + lx + 7L + xL)' equal to zero and attempt to solve: Simplifying -22l + lx + 7L + xL = 0 Reorder the terms: 7L + -22l + lx + xL = 0 Solving 7L + -22l + lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-7L' to each side of the equation. 7L + -22l + lx + -7L + xL = 0 + -7L Reorder the terms: 7L + -7L + -22l + lx + xL = 0 + -7L Combine like terms: 7L + -7L = 0 0 + -22l + lx + xL = 0 + -7L -22l + lx + xL = 0 + -7L Remove the zero: -22l + lx + xL = -7L Add '-1xL' to each side of the equation. -22l + lx + xL + -1xL = -7L + -1xL Combine like terms: xL + -1xL = 0 -22l + lx + 0 = -7L + -1xL -22l + lx = -7L + -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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