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Simplifying LNX + LN(X + -15) = LN(X + -63) Reorder the terms: LNX + LN(-15 + X) = LN(X + -63) LNX + (-15 * LN + X * LN) = LN(X + -63) LNX + (-15LN + LNX) = LN(X + -63) Reorder the terms: -15LN + LNX + LNX = LN(X + -63) Combine like terms: LNX + LNX = 2LNX -15LN + 2LNX = LN(X + -63) Reorder the terms: -15LN + 2LNX = LN(-63 + X) -15LN + 2LNX = (-63 * LN + X * LN) -15LN + 2LNX = (-63LN + LNX) Solving -15LN + 2LNX = -63LN + LNX Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '63LN' to each side of the equation. -15LN + 63LN + 2LNX = -63LN + 63LN + LNX Combine like terms: -15LN + 63LN = 48LN 48LN + 2LNX = -63LN + 63LN + LNX Combine like terms: -63LN + 63LN = 0 48LN + 2LNX = 0 + LNX 48LN + 2LNX = LNX Add '-1LNX' to each side of the equation. 48LN + 2LNX + -1LNX = LNX + -1LNX Combine like terms: 2LNX + -1LNX = 1LNX 48LN + 1LNX = LNX + -1LNX Combine like terms: LNX + -1LNX = 0 48LN + 1LNX = 0 Factor out the Greatest Common Factor (GCF), 'LN'. LN(48 + X) = 0Subproblem 1
Set the factor 'LN' equal to zero and attempt to solve: Simplifying LN = 0 Solving LN = 0 Move all terms containing L to the left, all other terms to the right. Simplifying LN = 0 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 '(48 + X)' equal to zero and attempt to solve: Simplifying 48 + X = 0 Solving 48 + X = 0 Move all terms containing L to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + X = 0 + -48 Combine like terms: 48 + -48 = 0 0 + X = 0 + -48 X = 0 + -48 Combine like terms: 0 + -48 = -48 X = -48 Add '-1X' to each side of the equation. X + -1X = -48 + -1X Combine like terms: X + -1X = 0 0 = -48 + -1X Simplifying 0 = -48 + -1X 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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