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Simplifying ln(x + 3) + ln(x + 4) = ln(110) Reorder the terms: ln(3 + x) + ln(x + 4) = ln(110) (3 * ln + x * ln) + ln(x + 4) = ln(110) (3ln + lnx) + ln(x + 4) = ln(110) Reorder the terms: 3ln + lnx + ln(4 + x) = ln(110) 3ln + lnx + (4 * ln + x * ln) = ln(110) 3ln + lnx + (4ln + lnx) = ln(110) Reorder the terms: 3ln + 4ln + lnx + lnx = ln(110) Combine like terms: 3ln + 4ln = 7ln 7ln + lnx + lnx = ln(110) Combine like terms: lnx + lnx = 2lnx 7ln + 2lnx = ln(110) Reorder the terms for easier multiplication: 7ln + 2lnx = 110ln Solving 7ln + 2lnx = 110ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-110ln' to each side of the equation. 7ln + -110ln + 2lnx = 110ln + -110ln Combine like terms: 7ln + -110ln = -103ln -103ln + 2lnx = 110ln + -110ln Combine like terms: 110ln + -110ln = 0 -103ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-103 + 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 '(-103 + 2x)' equal to zero and attempt to solve: Simplifying -103 + 2x = 0 Solving -103 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '103' to each side of the equation. -103 + 103 + 2x = 0 + 103 Combine like terms: -103 + 103 = 0 0 + 2x = 0 + 103 2x = 0 + 103 Combine like terms: 0 + 103 = 103 2x = 103 Add '-2x' to each side of the equation. 2x + -2x = 103 + -2x Combine like terms: 2x + -2x = 0 0 = 103 + -2x Simplifying 0 = 103 + -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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