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Simplifying ln(x + 1) + ln(x + 5) = ln(45) Reorder the terms: ln(1 + x) + ln(x + 5) = ln(45) (1 * ln + x * ln) + ln(x + 5) = ln(45) (1ln + lnx) + ln(x + 5) = ln(45) Reorder the terms: 1ln + lnx + ln(5 + x) = ln(45) 1ln + lnx + (5 * ln + x * ln) = ln(45) 1ln + lnx + (5ln + lnx) = ln(45) Reorder the terms: 1ln + 5ln + lnx + lnx = ln(45) Combine like terms: 1ln + 5ln = 6ln 6ln + lnx + lnx = ln(45) Combine like terms: lnx + lnx = 2lnx 6ln + 2lnx = ln(45) Reorder the terms for easier multiplication: 6ln + 2lnx = 45ln Solving 6ln + 2lnx = 45ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-45ln' to each side of the equation. 6ln + -45ln + 2lnx = 45ln + -45ln Combine like terms: 6ln + -45ln = -39ln -39ln + 2lnx = 45ln + -45ln Combine like terms: 45ln + -45ln = 0 -39ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-39 + 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 '(-39 + 2x)' equal to zero and attempt to solve: Simplifying -39 + 2x = 0 Solving -39 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + 2x = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 2x = 0 + 39 2x = 0 + 39 Combine like terms: 0 + 39 = 39 2x = 39 Add '-2x' to each side of the equation. 2x + -2x = 39 + -2x Combine like terms: 2x + -2x = 0 0 = 39 + -2x Simplifying 0 = 39 + -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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