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Simplifying ln(4 + 54e3x) = 0 (4 * ln + 54e3x * ln) = 0 Reorder the terms: (54e3lnx + 4ln) = 0 (54e3lnx + 4ln) = 0 Solving 54e3lnx + 4ln = 0 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-4ln' to each side of the equation. 54e3lnx + 4ln + -4ln = 0 + -4ln Combine like terms: 4ln + -4ln = 0 54e3lnx + 0 = 0 + -4ln 54e3lnx = 0 + -4ln Remove the zero: 54e3lnx = -4ln Divide each side by '54lnx'. e3 = -0.07407407407x-1 Simplifying e3 = -0.07407407407x-1 Combine like terms: -0.07407407407x-1 + 0.07407407407x-1 = 0.00000000000 e3 + 0.07407407407x-1 = 0.00000000000 Factor out the Greatest Common Factor (GCF), 'x-1'. x-1(e3x + 0.07407407407) = 0.00000000000Subproblem 1
Set the factor 'x-1' equal to zero and attempt to solve: Simplifying x-1 = 0 Solving x-1 = 0 Move all terms containing e to the left, all other terms to the right. Add '-1x-1' to each side of the equation. x-1 + -1x-1 = 0 + -1x-1 Remove the zero: 0 = -1x-1 Simplifying 0 = -1x-1 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 '(e3x + 0.07407407407)' equal to zero and attempt to solve: Simplifying e3x + 0.07407407407 = 0 Reorder the terms: 0.07407407407 + e3x = 0 Solving 0.07407407407 + e3x = 0 Move all terms containing e to the left, all other terms to the right. Add '-0.07407407407' to each side of the equation. 0.07407407407 + -0.07407407407 + e3x = 0 + -0.07407407407 Combine like terms: 0.07407407407 + -0.07407407407 = 0.00000000000 0.00000000000 + e3x = 0 + -0.07407407407 e3x = 0 + -0.07407407407 Combine like terms: 0 + -0.07407407407 = -0.07407407407 e3x = -0.07407407407 Divide each side by 'x'. e3 = -0.07407407407x-1 Simplifying e3 = -0.07407407407x-1 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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