ln(x-5)+ln(2)=ln(14)

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Solution for ln(x-5)+ln(2)=ln(14) equation: 


Simplifying
ln(x + -5) + ln(2) = ln(14)

Reorder the terms:
ln(-5 + x) + ln(2) = ln(14)
(-5 * ln + x * ln) + ln(2) = ln(14)
(-5ln + lnx) + ln(2) = ln(14)

Reorder the terms for easier multiplication:
-5ln + lnx + 2ln = ln(14)

Reorder the terms:
-5ln + 2ln + lnx = ln(14)

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

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

Solving
-3ln + 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.
-3ln + -14ln + lnx = 14ln + -14ln

Combine like terms: -3ln + -14ln = -17ln
-17ln + lnx = 14ln + -14ln

Combine like terms: 14ln + -14ln = 0
-17ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-17 + 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 '(-17 + x)' equal to zero and attempt to solve:

Simplifying
-17 + x = 0

Solving
-17 + x = 0

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

Add '17' to each side of the equation.
-17 + 17 + x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + x = 0 + 17
x = 0 + 17

Combine like terms: 0 + 17 = 17
x = 17

Add '-1x' to each side of the equation.
x + -1x = 17 + -1x

Combine like terms: x + -1x = 0
0 = 17 + -1x

Simplifying
0 = 17 + -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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