ln(5x-100)=lnx

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Solution for ln(5x-100)=lnx equation: 


Simplifying
ln(5x + -100) = lnx

Reorder the terms:
ln(-100 + 5x) = lnx
(-100 * ln + 5x * ln) = lnx
(-100ln + 5lnx) = lnx

Solving
-100ln + 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.
-100ln + 5lnx + -1lnx = lnx + -1lnx

Combine like terms: 5lnx + -1lnx = 4lnx
-100ln + 4lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-100ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), '4ln'.
4ln(-25 + x) = 0

Ignore the factor 4.

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 '(-25 + x)' equal to zero and attempt to solve:

Simplifying
-25 + x = 0

Solving
-25 + x = 0

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

Add '25' to each side of the equation.
-25 + 25 + x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + x = 0 + 25
x = 0 + 25

Combine like terms: 0 + 25 = 25
x = 25

Add '-1x' to each side of the equation.
x + -1x = 25 + -1x

Combine like terms: x + -1x = 0
0 = 25 + -1x

Simplifying
0 = 25 + -1x

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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