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Simplifying 5ln(6x) = lne4 Remove parenthesis around (6x) 5ln * 6x = lne4 Reorder the terms for easier multiplication: 5 * 6ln * x = lne4 Multiply 5 * 6 30ln * x = lne4 Multiply ln * x 30lnx = lne4 Solving 30lnx = e4ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1e4ln' to each side of the equation. -1e4ln + 30lnx = e4ln + -1e4ln Combine like terms: e4ln + -1e4ln = 0 -1e4ln + 30lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1e4 + 30x) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 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 '(-1e4 + 30x)' equal to zero and attempt to solve: Simplifying -1e4 + 30x = 0 Solving -1e4 + 30x = 0 Move all terms containing l to the left, all other terms to the right. Add 'e4' to each side of the equation. -1e4 + e4 + 30x = 0 + e4 Combine like terms: -1e4 + e4 = 0 0 + 30x = 0 + e4 30x = 0 + e4 Remove the zero: 30x = e4 Add '-30x' to each side of the equation. 30x + -30x = e4 + -30x Combine like terms: 30x + -30x = 0 0 = e4 + -30x Simplifying 0 = e4 + -30x 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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