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Simplifying ln(2x) + ln(2x2) + ln(2x3) = 6 Remove parenthesis around (2x) ln * 2x + ln(2x2) + ln(2x3) = 6 Reorder the terms for easier multiplication: 2ln * x + ln(2x2) + ln(2x3) = 6 Multiply ln * x 2lnx + ln(2x2) + ln(2x3) = 6 Remove parenthesis around (2x2) 2lnx + ln * 2x2 + ln(2x3) = 6 Reorder the terms for easier multiplication: 2lnx + 2ln * x2 + ln(2x3) = 6 Multiply ln * x2 2lnx + 2lnx2 + ln(2x3) = 6 Remove parenthesis around (2x3) 2lnx + 2lnx2 + ln * 2x3 = 6 Reorder the terms for easier multiplication: 2lnx + 2lnx2 + 2ln * x3 = 6 Multiply ln * x3 2lnx + 2lnx2 + 2lnx3 = 6 Solving 2lnx + 2lnx2 + 2lnx3 = 6 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -6 + 2lnx + 2lnx2 + 2lnx3 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 2lnx + 2lnx2 + 2lnx3 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + lnx + lnx2 + lnx3) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + lnx + lnx2 + lnx3)' equal to zero and attempt to solve: Simplifying -3 + lnx + lnx2 + lnx3 = 0 Solving -3 + lnx + lnx2 + lnx3 = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + lnx + lnx2 + 3 + lnx3 = 0 + 3 Reorder the terms: -3 + 3 + lnx + lnx2 + lnx3 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + lnx + lnx2 + lnx3 = 0 + 3 lnx + lnx2 + lnx3 = 0 + 3 Combine like terms: 0 + 3 = 3 lnx + lnx2 + lnx3 = 3 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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