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Simplifying ln(x + -15) + ln(x + 48) = 3ln(4) Reorder the terms: ln(-15 + x) + ln(x + 48) = 3ln(4) (-15 * ln + x * ln) + ln(x + 48) = 3ln(4) (-15ln + lnx) + ln(x + 48) = 3ln(4) Reorder the terms: -15ln + lnx + ln(48 + x) = 3ln(4) -15ln + lnx + (48 * ln + x * ln) = 3ln(4) -15ln + lnx + (48ln + lnx) = 3ln(4) Reorder the terms: -15ln + 48ln + lnx + lnx = 3ln(4) Combine like terms: -15ln + 48ln = 33ln 33ln + lnx + lnx = 3ln(4) Combine like terms: lnx + lnx = 2lnx 33ln + 2lnx = 3ln(4) Reorder the terms for easier multiplication: 33ln + 2lnx = 3 * 4ln Multiply 3 * 4 33ln + 2lnx = 12ln Solving 33ln + 2lnx = 12ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. 33ln + -12ln + 2lnx = 12ln + -12ln Combine like terms: 33ln + -12ln = 21ln 21ln + 2lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 21ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(21 + 2x) = 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 '(21 + 2x)' equal to zero and attempt to solve: Simplifying 21 + 2x = 0 Solving 21 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 2x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 2x = 0 + -21 2x = 0 + -21 Combine like terms: 0 + -21 = -21 2x = -21 Add '-2x' to each side of the equation. 2x + -2x = -21 + -2x Combine like terms: 2x + -2x = 0 0 = -21 + -2x Simplifying 0 = -21 + -2x 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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