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Simplifying ln(2x + 1) + ln(x + 8) = 3 Reorder the terms: ln(1 + 2x) + ln(x + 8) = 3 (1 * ln + 2x * ln) + ln(x + 8) = 3 (1ln + 2lnx) + ln(x + 8) = 3 Reorder the terms: 1ln + 2lnx + ln(8 + x) = 3 1ln + 2lnx + (8 * ln + x * ln) = 3 1ln + 2lnx + (8ln + lnx) = 3 Reorder the terms: 1ln + 8ln + 2lnx + lnx = 3 Combine like terms: 1ln + 8ln = 9ln 9ln + 2lnx + lnx = 3 Combine like terms: 2lnx + lnx = 3lnx 9ln + 3lnx = 3 Solving 9ln + 3lnx = 3 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -3 + 9ln + 3lnx = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 9ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 3ln + lnx) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 3ln + lnx)' equal to zero and attempt to solve: Simplifying -1 + 3ln + lnx = 0 Solving -1 + 3ln + lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 3ln + 1 + lnx = 0 + 1 Reorder the terms: -1 + 1 + 3ln + lnx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3ln + lnx = 0 + 1 3ln + lnx = 0 + 1 Combine like terms: 0 + 1 = 1 3ln + lnx = 1 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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