ln(x-3)+ln(5)=ln(14)

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Solution for ln(x-3)+ln(5)=ln(14) equation: 


Simplifying
ln(x + -3) + ln(5) = ln(14)

Reorder the terms:
ln(-3 + x) + ln(5) = ln(14)
(-3 * ln + x * ln) + ln(5) = ln(14)
(-3ln + lnx) + ln(5) = ln(14)

Reorder the terms for easier multiplication:
-3ln + lnx + 5ln = ln(14)

Reorder the terms:
-3ln + 5ln + lnx = ln(14)

Combine like terms: -3ln + 5ln = 2ln
2ln + lnx = ln(14)

Reorder the terms for easier multiplication:
2ln + lnx = 14ln

Solving
2ln + lnx = 14ln

Solving for variable 'l'.

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

Add '-14ln' to each side of the equation.
2ln + -14ln + lnx = 14ln + -14ln

Combine like terms: 2ln + -14ln = -12ln
-12ln + lnx = 14ln + -14ln

Combine like terms: 14ln + -14ln = 0
-12ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-12 + x) = 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 '(-12 + x)' equal to zero and attempt to solve:

Simplifying
-12 + x = 0

Solving
-12 + x = 0

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

Add '12' to each side of the equation.
-12 + 12 + x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + x = 0 + 12
x = 0 + 12

Combine like terms: 0 + 12 = 12
x = 12

Add '-1x' to each side of the equation.
x + -1x = 12 + -1x

Combine like terms: x + -1x = 0
0 = 12 + -1x

Simplifying
0 = 12 + -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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