ln(x-2)+ln(x-5)=ln(18)

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Solution for ln(x-2)+ln(x-5)=ln(18) equation: 


Simplifying
ln(x + -2) + ln(x + -5) = ln(18)

Reorder the terms:
ln(-2 + x) + ln(x + -5) = ln(18)
(-2 * ln + x * ln) + ln(x + -5) = ln(18)
(-2ln + lnx) + ln(x + -5) = ln(18)

Reorder the terms:
-2ln + lnx + ln(-5 + x) = ln(18)
-2ln + lnx + (-5 * ln + x * ln) = ln(18)
-2ln + lnx + (-5ln + lnx) = ln(18)

Reorder the terms:
-2ln + -5ln + lnx + lnx = ln(18)

Combine like terms: -2ln + -5ln = -7ln
-7ln + lnx + lnx = ln(18)

Combine like terms: lnx + lnx = 2lnx
-7ln + 2lnx = ln(18)

Reorder the terms for easier multiplication:
-7ln + 2lnx = 18ln

Solving
-7ln + 2lnx = 18ln

Solving for variable 'l'.

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

Add '-18ln' to each side of the equation.
-7ln + -18ln + 2lnx = 18ln + -18ln

Combine like terms: -7ln + -18ln = -25ln
-25ln + 2lnx = 18ln + -18ln

Combine like terms: 18ln + -18ln = 0
-25ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-25 + 2x) = 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 '(-25 + 2x)' equal to zero and attempt to solve:

Simplifying
-25 + 2x = 0

Solving
-25 + 2x = 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 + 2x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 2x = 0 + 25
2x = 0 + 25

Combine like terms: 0 + 25 = 25
2x = 25

Add '-2x' to each side of the equation.
2x + -2x = 25 + -2x

Combine like terms: 2x + -2x = 0
0 = 25 + -2x

Simplifying
0 = 25 + -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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