ln(x-4)+ln(5x)=ln(25)

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Solution for ln(x-4)+ln(5x)=ln(25) equation: 


Simplifying
ln(x + -4) + ln(5x) = ln(25)

Reorder the terms:
ln(-4 + x) + ln(5x) = ln(25)
(-4 * ln + x * ln) + ln(5x) = ln(25)
(-4ln + lnx) + ln(5x) = ln(25)

Remove parenthesis around (5x)
-4ln + lnx + ln * 5x = ln(25)

Reorder the terms for easier multiplication:
-4ln + lnx + 5ln * x = ln(25)

Multiply ln * x
-4ln + lnx + 5lnx = ln(25)

Combine like terms: lnx + 5lnx = 6lnx
-4ln + 6lnx = ln(25)

Reorder the terms for easier multiplication:
-4ln + 6lnx = 25ln

Solving
-4ln + 6lnx = 25ln

Solving for variable 'l'.

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

Add '-25ln' to each side of the equation.
-4ln + -25ln + 6lnx = 25ln + -25ln

Combine like terms: -4ln + -25ln = -29ln
-29ln + 6lnx = 25ln + -25ln

Combine like terms: 25ln + -25ln = 0
-29ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-29 + 6x) = 0


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 '(-29 + 6x)' equal to zero and attempt to solve:

Simplifying
-29 + 6x = 0

Solving
-29 + 6x = 0

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

Add '29' to each side of the equation.
-29 + 29 + 6x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 6x = 0 + 29
6x = 0 + 29

Combine like terms: 0 + 29 = 29
6x = 29

Add '-6x' to each side of the equation.
6x + -6x = 29 + -6x

Combine like terms: 6x + -6x = 0
0 = 29 + -6x

Simplifying
0 = 29 + -6x

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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