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Simplifying Ln(x2 + -10) = ln(x) + ln(3) Reorder the terms: nL(-10 + x2) = ln(x) + ln(3) (-10 * nL + x2 * nL) = ln(x) + ln(3) (-10nL + nx2L) = ln(x) + ln(3) Multiply ln * x -10nL + nx2L = lnx + ln(3) Reorder the terms for easier multiplication: -10nL + nx2L = lnx + 3ln Reorder the terms: -10nL + nx2L = 3ln + lnx Solving -10nL + nx2L = 3ln + lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3ln' to each side of the equation. -10nL + -3ln + nx2L = 3ln + -3ln + lnx Reorder the terms: -3ln + -10nL + nx2L = 3ln + -3ln + lnx Combine like terms: 3ln + -3ln = 0 -3ln + -10nL + nx2L = 0 + lnx -3ln + -10nL + nx2L = lnx Add '-1lnx' to each side of the equation. -3ln + -10nL + -1lnx + nx2L = lnx + -1lnx Reorder the terms: -3ln + -1lnx + -10nL + nx2L = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -3ln + -1lnx + -10nL + nx2L = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-3l + -1lx + -10L + x2L) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-3l + -1lx + -10L + x2L)' equal to zero and attempt to solve: Simplifying -3l + -1lx + -10L + x2L = 0 Reorder the terms: -10L + -3l + -1lx + x2L = 0 Solving -10L + -3l + -1lx + x2L = 0 Move all terms containing n to the left, all other terms to the right. Add '10L' to each side of the equation. -10L + -3l + -1lx + 10L + x2L = 0 + 10L Reorder the terms: -10L + 10L + -3l + -1lx + x2L = 0 + 10L Combine like terms: -10L + 10L = 0 0 + -3l + -1lx + x2L = 0 + 10L -3l + -1lx + x2L = 0 + 10L Remove the zero: -3l + -1lx + x2L = 10L Add '3l' to each side of the equation. -3l + -1lx + 3l + x2L = 10L + 3l Reorder the terms: -3l + 3l + -1lx + x2L = 10L + 3l Combine like terms: -3l + 3l = 0 0 + -1lx + x2L = 10L + 3l -1lx + x2L = 10L + 3l Add 'lx' to each side of the equation. -1lx + lx + x2L = 10L + 3l + lx Combine like terms: -1lx + lx = 0 0 + x2L = 10L + 3l + lx x2L = 10L + 3l + lx Add '-1x2L' to each side of the equation. x2L + -1x2L = 10L + 3l + lx + -1x2L Combine like terms: x2L + -1x2L = 0 0 = 10L + 3l + lx + -1x2L Simplifying 0 = 10L + 3l + lx + -1x2L The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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