5lne-lne^3=

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Solution for 5lne-lne^3= equation:


Simplifying
5lne + -1lne3 = 0

Solving
5eln + -1e3ln = 0

Solving for variable 'e'.

Factor out the Greatest Common Factor (GCF), 'eln'.
eln(5 + -1e2) = 0

Subproblem 1

Set the factor 'eln' equal to zero and attempt to solve: Simplifying eln = 0 Solving eln = 0 Move all terms containing e to the left, all other terms to the right. Simplifying eln = 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 '(5 + -1e2)' equal to zero and attempt to solve: Simplifying 5 + -1e2 = 0 Solving 5 + -1e2 = 0 Move all terms containing e to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1e2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1e2 = 0 + -5 -1e2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1e2 = -5 Divide each side by '-1'. e2 = 5 Simplifying e2 = 5 Take the square root of each side: e = {-2.236067978, 2.236067978}

Solution

e = {-2.236067978, 2.236067978}

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