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