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Simplifying ln(x) + ln(x + 7) = ln(63) Multiply ln * x lnx + ln(x + 7) = ln(63) Reorder the terms: lnx + ln(7 + x) = ln(63) lnx + (7 * ln + x * ln) = ln(63) lnx + (7ln + lnx) = ln(63) Reorder the terms: 7ln + lnx + lnx = ln(63) Combine like terms: lnx + lnx = 2lnx 7ln + 2lnx = ln(63) Reorder the terms for easier multiplication: 7ln + 2lnx = 63ln Solving 7ln + 2lnx = 63ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-63ln' to each side of the equation. 7ln + -63ln + 2lnx = 63ln + -63ln Combine like terms: 7ln + -63ln = -56ln -56ln + 2lnx = 63ln + -63ln Combine like terms: 63ln + -63ln = 0 -56ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-28 + x) = 0 Ignore the factor 2.Subproblem 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 '(-28 + x)' equal to zero and attempt to solve: Simplifying -28 + x = 0 Solving -28 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = 0 + 28 Combine like terms: -28 + 28 = 0 0 + x = 0 + 28 x = 0 + 28 Combine like terms: 0 + 28 = 28 x = 28 Add '-1x' to each side of the equation. x + -1x = 28 + -1x Combine like terms: x + -1x = 0 0 = 28 + -1x Simplifying 0 = 28 + -1x 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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