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Simplifying 3ln(x2) = 7ln(4x) Multiply ln * x2 3lnx2 = 7ln(4x) Remove parenthesis around (4x) 3lnx2 = 7ln * 4x Reorder the terms for easier multiplication: 3lnx2 = 7 * 4ln * x Multiply 7 * 4 3lnx2 = 28ln * x Multiply ln * x 3lnx2 = 28lnx Solving 3lnx2 = 28lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-28lnx' to each side of the equation. -28lnx + 3lnx2 = 28lnx + -28lnx Combine like terms: 28lnx + -28lnx = 0 -28lnx + 3lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'lnx'. lnx(-28 + 3x) = 0Subproblem 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 '(-28 + 3x)' equal to zero and attempt to solve: Simplifying -28 + 3x = 0 Solving -28 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + 3x = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 3x = 0 + 28 3x = 0 + 28 Combine like terms: 0 + 28 = 28 3x = 28 Add '-3x' to each side of the equation. 3x + -3x = 28 + -3x Combine like terms: 3x + -3x = 0 0 = 28 + -3x Simplifying 0 = 28 + -3x 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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