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Simplifying ln(y) = 3ln(x2 + 4) + ln(32) + -3ln(4) Multiply ln * y lny = 3ln(x2 + 4) + ln(32) + -3ln(4) Reorder the terms: lny = 3ln(4 + x2) + ln(32) + -3ln(4) lny = (4 * 3ln + x2 * 3ln) + ln(32) + -3ln(4) lny = (12ln + 3lnx2) + ln(32) + -3ln(4) Reorder the terms for easier multiplication: lny = 12ln + 3lnx2 + 32ln + -3ln(4) Reorder the terms for easier multiplication: lny = 12ln + 3lnx2 + 32ln + -3 * 4ln Multiply -3 * 4 lny = 12ln + 3lnx2 + 32ln + -12ln Reorder the terms: lny = 12ln + 32ln + -12ln + 3lnx2 Combine like terms: 12ln + 32ln = 44ln lny = 44ln + -12ln + 3lnx2 Combine like terms: 44ln + -12ln = 32ln lny = 32ln + 3lnx2 Solving lny = 32ln + 3lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-32ln' to each side of the equation. -32ln + lny = 32ln + -32ln + 3lnx2 Combine like terms: 32ln + -32ln = 0 -32ln + lny = 0 + 3lnx2 -32ln + lny = 3lnx2 Add '-3lnx2' to each side of the equation. -32ln + -3lnx2 + lny = 3lnx2 + -3lnx2 Combine like terms: 3lnx2 + -3lnx2 = 0 -32ln + -3lnx2 + lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-32 + -3x2 + y) = 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 '(-32 + -3x2 + y)' equal to zero and attempt to solve: Simplifying -32 + -3x2 + y = 0 Solving -32 + -3x2 + y = 0 Move all terms containing l to the left, all other terms to the right. Add '32' to each side of the equation. -32 + -3x2 + 32 + y = 0 + 32 Reorder the terms: -32 + 32 + -3x2 + y = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -3x2 + y = 0 + 32 -3x2 + y = 0 + 32 Combine like terms: 0 + 32 = 32 -3x2 + y = 32 Add '3x2' to each side of the equation. -3x2 + 3x2 + y = 32 + 3x2 Combine like terms: -3x2 + 3x2 = 0 0 + y = 32 + 3x2 y = 32 + 3x2 Add '-1y' to each side of the equation. y + -1y = 32 + 3x2 + -1y Combine like terms: y + -1y = 0 0 = 32 + 3x2 + -1y Simplifying 0 = 32 + 3x2 + -1y 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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