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Simplifying 8ln(x + 1) = ln(x + 1) + 7 Reorder the terms: 8ln(1 + x) = ln(x + 1) + 7 (1 * 8ln + x * 8ln) = ln(x + 1) + 7 (8ln + 8lnx) = ln(x + 1) + 7 Reorder the terms: 8ln + 8lnx = ln(1 + x) + 7 8ln + 8lnx = (1 * ln + x * ln) + 7 8ln + 8lnx = (1ln + lnx) + 7 Reorder the terms: 8ln + 8lnx = 7 + 1ln + lnx Solving 8ln + 8lnx = 7 + 1ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 8ln + -1ln + 8lnx = 7 + 1ln + -1ln + lnx Combine like terms: 8ln + -1ln = 7ln 7ln + 8lnx = 7 + 1ln + -1ln + lnx Combine like terms: 1ln + -1ln = 0 7ln + 8lnx = 7 + 0 + lnx 7ln + 8lnx = 7 + lnx Add '-1lnx' to each side of the equation. 7ln + 8lnx + -1lnx = 7 + lnx + -1lnx Combine like terms: 8lnx + -1lnx = 7lnx 7ln + 7lnx = 7 + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 7ln + 7lnx = 7 + 0 7ln + 7lnx = 7 Reorder the terms: -7 + 7ln + 7lnx = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 7ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-1 + ln + lnx) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-1 + ln + lnx)' equal to zero and attempt to solve: Simplifying -1 + ln + lnx = 0 Solving -1 + ln + 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 + ln + 1 + lnx = 0 + 1 Reorder the terms: -1 + 1 + ln + lnx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + ln + lnx = 0 + 1 ln + lnx = 0 + 1 Combine like terms: 0 + 1 = 1 ln + 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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