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Simplifying ln(sqrt(x)) + 1.5lnx = ln(2x) Multiply qrst * x ln(qrstx) + 1.5lnx = ln(2x) Multiply ln * qrstx lnqrstx + 1.5lnx = ln(2x) Remove parenthesis around (2x) lnqrstx + 1.5lnx = ln * 2x Reorder the terms for easier multiplication: lnqrstx + 1.5lnx = 2ln * x Multiply ln * x lnqrstx + 1.5lnx = 2lnx Solving lnqrstx + 1.5lnx = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. lnqrstx + 1.5lnx + -2lnx = 2lnx + -2lnx Combine like terms: 1.5lnx + -2lnx = -0.5lnx lnqrstx + -0.5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 lnqrstx + -0.5lnx = 0 Factor out the Greatest Common Factor (GCF), 'lnx'. lnx(qrst + -0.5) = 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 '(qrst + -0.5)' equal to zero and attempt to solve: Simplifying qrst + -0.5 = 0 Reorder the terms: -0.5 + qrst = 0 Solving -0.5 + qrst = 0 Move all terms containing l to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + qrst = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + qrst = 0 + 0.5 qrst = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 qrst = 0.5 Add '-1qrst' to each side of the equation. qrst + -1qrst = 0.5 + -1qrst Combine like terms: qrst + -1qrst = 0 0 = 0.5 + -1qrst Simplifying 0 = 0.5 + -1qrst 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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