ln(2e^3x)=ln(1016)

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Solution for ln(2e^3x)=ln(1016) equation:


Simplifying
ln(2e3x) = ln(1016)

Remove parenthesis around (2e3x)
ln * 2e3x = ln(1016)

Reorder the terms for easier multiplication:
2ln * e3x = ln(1016)

Multiply ln * e3x
2e3lnx = ln(1016)

Reorder the terms for easier multiplication:
2e3lnx = 1016ln

Solving
2e3lnx = 1016ln

Solving for variable 'e'.

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

Divide each side by '2lnx'.
e3 = 508x-1

Simplifying
e3 = 508x-1

Combine like terms: 508x-1 + -508x-1 = 0
e3 + -508x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e3x + -508) = 0

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 + -508)' equal to zero and attempt to solve: Simplifying e3x + -508 = 0 Reorder the terms: -508 + e3x = 0 Solving -508 + e3x = 0 Move all terms containing e to the left, all other terms to the right. Add '508' to each side of the equation. -508 + 508 + e3x = 0 + 508 Combine like terms: -508 + 508 = 0 0 + e3x = 0 + 508 e3x = 0 + 508 Combine like terms: 0 + 508 = 508 e3x = 508 Divide each side by 'x'. e3 = 508x-1 Simplifying e3 = 508x-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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