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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