ln(5x-2)=ln(x)

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Solution for ln(5x-2)=ln(x) equation: 


Simplifying
ln(5x + -2) = ln(x)

Reorder the terms:
ln(-2 + 5x) = ln(x)
(-2 * ln + 5x * ln) = ln(x)
(-2ln + 5lnx) = ln(x)

Multiply ln * x
-2ln + 5lnx = lnx

Solving
-2ln + 5lnx = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
-2ln + 5lnx + -1lnx = lnx + -1lnx

Combine like terms: 5lnx + -1lnx = 4lnx
-2ln + 4lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-2ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-1 + 2x) = 0

Ignore the factor 2.

Subproblem 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 '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2x = 0 + 1

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

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

Add '-2x' to each side of the equation.
2x + -2x = 1 + -2x

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

Simplifying
0 = 1 + -2x

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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