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Simplifying ln(x + 7) + ln(x + 3) = ln * 77 Reorder the terms: ln(7 + x) + ln(x + 3) = ln * 77 (7 * ln + x * ln) + ln(x + 3) = ln * 77 (7ln + lnx) + ln(x + 3) = ln * 77 Reorder the terms: 7ln + lnx + ln(3 + x) = ln * 77 7ln + lnx + (3 * ln + x * ln) = ln * 77 7ln + lnx + (3ln + lnx) = ln * 77 Reorder the terms: 7ln + 3ln + lnx + lnx = ln * 77 Combine like terms: 7ln + 3ln = 10ln 10ln + lnx + lnx = ln * 77 Combine like terms: lnx + lnx = 2lnx 10ln + 2lnx = ln * 77 Reorder the terms for easier multiplication: 10ln + 2lnx = 77ln Solving 10ln + 2lnx = 77ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-77ln' to each side of the equation. 10ln + -77ln + 2lnx = 77ln + -77ln Combine like terms: 10ln + -77ln = -67ln -67ln + 2lnx = 77ln + -77ln Combine like terms: 77ln + -77ln = 0 -67ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-67 + 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 '(-67 + 2x)' equal to zero and attempt to solve: Simplifying -67 + 2x = 0 Solving -67 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '67' to each side of the equation. -67 + 67 + 2x = 0 + 67 Combine like terms: -67 + 67 = 0 0 + 2x = 0 + 67 2x = 0 + 67 Combine like terms: 0 + 67 = 67 2x = 67 Add '-2x' to each side of the equation. 2x + -2x = 67 + -2x Combine like terms: 2x + -2x = 0 0 = 67 + -2x Simplifying 0 = 67 + -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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