500=4e^3x-1

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Solution for 500=4e^3x-1 equation:


Simplifying
500 = 4e3x + -1

Reorder the terms:
500 = -1 + 4e3x

Solving
500 = -1 + 4e3x

Solving for variable 'e'.

Move all terms containing e to the left, all other terms to the right.

Add '-4e3x' to each side of the equation.
500 + -4e3x = -1 + 4e3x + -4e3x

Combine like terms: 4e3x + -4e3x = 0
500 + -4e3x = -1 + 0
500 + -4e3x = -1

Add '-500' to each side of the equation.
500 + -500 + -4e3x = -1 + -500

Combine like terms: 500 + -500 = 0
0 + -4e3x = -1 + -500
-4e3x = -1 + -500

Combine like terms: -1 + -500 = -501
-4e3x = -501

Divide each side by '-4x'.
e3 = 125.25x-1

Simplifying
e3 = 125.25x-1

Combine like terms: 125.25x-1 + -125.25x-1 = 0.00
e3 + -125.25x-1 = 0.00

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e3x + -125.25) = 0.00

Subproblem 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 + -125.25)' equal to zero and attempt to solve: Simplifying e3x + -125.25 = 0 Reorder the terms: -125.25 + e3x = 0 Solving -125.25 + e3x = 0 Move all terms containing e to the left, all other terms to the right. Add '125.25' to each side of the equation. -125.25 + 125.25 + e3x = 0 + 125.25 Combine like terms: -125.25 + 125.25 = 0.00 0.00 + e3x = 0 + 125.25 e3x = 0 + 125.25 Combine like terms: 0 + 125.25 = 125.25 e3x = 125.25 Divide each side by 'x'. e3 = 125.25x-1 Simplifying e3 = 125.25x-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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