ln(4e^2x)=ln(8)

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Solution for ln(4e^2x)=ln(8) equation: 


Simplifying
ln(4e2x) = ln(8)

Remove parenthesis around (4e2x)
ln * 4e2x = ln(8)

Reorder the terms for easier multiplication:
4ln * e2x = ln(8)

Multiply ln * e2x
4e2lnx = ln(8)

Reorder the terms for easier multiplication:
4e2lnx = 8ln

Solving
4e2lnx = 8ln

Solving for variable 'e'.

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

Divide each side by '4lnx'.
e2 = 2x-1

Simplifying
e2 = 2x-1

Combine like terms: 2x-1 + -2x-1 = 0
e2 + -2x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -2) = 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 '(e2x + -2)' equal to zero and attempt to solve:

Simplifying
e2x + -2 = 0

Reorder the terms:
-2 + e2x = 0

Solving
-2 + e2x = 0

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

Add '2' to each side of the equation.
-2 + 2 + e2x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + e2x = 0 + 2
e2x = 0 + 2

Combine like terms: 0 + 2 = 2
e2x = 2

Divide each side by 'x'.
e2 = 2x-1

Simplifying
e2 = 2x-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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