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Simplifying ln(5x) + ln(2 + x) = 4 Remove parenthesis around (5x) ln * 5x + ln(2 + x) = 4 Reorder the terms for easier multiplication: 5ln * x + ln(2 + x) = 4 Multiply ln * x 5lnx + ln(2 + x) = 4 5lnx + (2 * ln + x * ln) = 4 5lnx + (2ln + lnx) = 4 Reorder the terms: 2ln + 5lnx + lnx = 4 Combine like terms: 5lnx + lnx = 6lnx 2ln + 6lnx = 4 Solving 2ln + 6lnx = 4 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -4 + 2ln + 6lnx = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 2ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + ln + 3lnx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + ln + 3lnx)' equal to zero and attempt to solve: Simplifying -2 + ln + 3lnx = 0 Solving -2 + ln + 3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + ln + 2 + 3lnx = 0 + 2 Reorder the terms: -2 + 2 + ln + 3lnx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + ln + 3lnx = 0 + 2 ln + 3lnx = 0 + 2 Combine like terms: 0 + 2 = 2 ln + 3lnx = 2 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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