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Simplifying x * ln(8x3) + ln(8x2) = 20 + -1ln(2) Remove parenthesis around (8x3) x * ln * 8x3 + ln(8x2) = 20 + -1ln(2) Reorder the terms for easier multiplication: 8x * ln * x3 + ln(8x2) = 20 + -1ln(2) Multiply x * ln 8lnx * x3 + ln(8x2) = 20 + -1ln(2) Multiply lnx * x3 8lnx4 + ln(8x2) = 20 + -1ln(2) Remove parenthesis around (8x2) 8lnx4 + ln * 8x2 = 20 + -1ln(2) Reorder the terms for easier multiplication: 8lnx4 + 8ln * x2 = 20 + -1ln(2) Multiply ln * x2 8lnx4 + 8lnx2 = 20 + -1ln(2) Reorder the terms: 8lnx2 + 8lnx4 = 20 + -1ln(2) Reorder the terms for easier multiplication: 8lnx2 + 8lnx4 = 20 + -1 * 2ln Multiply -1 * 2 8lnx2 + 8lnx4 = 20 + -2ln Solving 8lnx2 + 8lnx4 = 20 + -2ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. 8lnx2 + 2ln + 8lnx4 = 20 + -2ln + 2ln Reorder the terms: 2ln + 8lnx2 + 8lnx4 = 20 + -2ln + 2ln Combine like terms: -2ln + 2ln = 0 2ln + 8lnx2 + 8lnx4 = 20 + 0 2ln + 8lnx2 + 8lnx4 = 20 Reorder the terms: -20 + 2ln + 8lnx2 + 8lnx4 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 2ln + 8lnx2 + 8lnx4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + ln + 4lnx2 + 4lnx4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + ln + 4lnx2 + 4lnx4)' equal to zero and attempt to solve: Simplifying -10 + ln + 4lnx2 + 4lnx4 = 0 Solving -10 + ln + 4lnx2 + 4lnx4 = 0 Move all terms containing l to the left, all other terms to the right. Add '10' to each side of the equation. -10 + ln + 4lnx2 + 10 + 4lnx4 = 0 + 10 Reorder the terms: -10 + 10 + ln + 4lnx2 + 4lnx4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + ln + 4lnx2 + 4lnx4 = 0 + 10 ln + 4lnx2 + 4lnx4 = 0 + 10 Combine like terms: 0 + 10 = 10 ln + 4lnx2 + 4lnx4 = 10 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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