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Simplifying ln(4x) + ln(5 + x) = 5 Remove parenthesis around (4x) ln * 4x + ln(5 + x) = 5 Reorder the terms for easier multiplication: 4ln * x + ln(5 + x) = 5 Multiply ln * x 4lnx + ln(5 + x) = 5 4lnx + (5 * ln + x * ln) = 5 4lnx + (5ln + lnx) = 5 Reorder the terms: 5ln + 4lnx + lnx = 5 Combine like terms: 4lnx + lnx = 5lnx 5ln + 5lnx = 5 Solving 5ln + 5lnx = 5 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -5 + 5ln + 5lnx = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 5ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + ln + lnx) = 0 Ignore the factor 5.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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