ln(x)+ln(x-7)=ln(7x-45)

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Solution for ln(x)+ln(x-7)=ln(7x-45) equation:


Simplifying
ln(x) + ln(x + -7) = ln(7x + -45)

Multiply ln * x
lnx + ln(x + -7) = ln(7x + -45)

Reorder the terms:
lnx + ln(-7 + x) = ln(7x + -45)
lnx + (-7 * ln + x * ln) = ln(7x + -45)
lnx + (-7ln + lnx) = ln(7x + -45)

Reorder the terms:
-7ln + lnx + lnx = ln(7x + -45)

Combine like terms: lnx + lnx = 2lnx
-7ln + 2lnx = ln(7x + -45)

Reorder the terms:
-7ln + 2lnx = ln(-45 + 7x)
-7ln + 2lnx = (-45 * ln + 7x * ln)
-7ln + 2lnx = (-45ln + 7lnx)

Solving
-7ln + 2lnx = -45ln + 7lnx

Solving for variable 'l'.

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

Add '45ln' to each side of the equation.
-7ln + 45ln + 2lnx = -45ln + 45ln + 7lnx

Combine like terms: -7ln + 45ln = 38ln
38ln + 2lnx = -45ln + 45ln + 7lnx

Combine like terms: -45ln + 45ln = 0
38ln + 2lnx = 0 + 7lnx
38ln + 2lnx = 7lnx

Add '-7lnx' to each side of the equation.
38ln + 2lnx + -7lnx = 7lnx + -7lnx

Combine like terms: 2lnx + -7lnx = -5lnx
38ln + -5lnx = 7lnx + -7lnx

Combine like terms: 7lnx + -7lnx = 0
38ln + -5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(38 + -5x) = 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 '(38 + -5x)' equal to zero and attempt to solve: Simplifying 38 + -5x = 0 Solving 38 + -5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + -5x = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -5x = 0 + -38 -5x = 0 + -38 Combine like terms: 0 + -38 = -38 -5x = -38 Add '5x' to each side of the equation. -5x + 5x = -38 + 5x Combine like terms: -5x + 5x = 0 0 = -38 + 5x Simplifying 0 = -38 + 5x 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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