ln(x)+ln(x-3)=ln(40)

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Solution for ln(x)+ln(x-3)=ln(40) equation: 


Simplifying
ln(x) + ln(x + -3) = ln(40)

Multiply ln * x
lnx + ln(x + -3) = ln(40)

Reorder the terms:
lnx + ln(-3 + x) = ln(40)
lnx + (-3 * ln + x * ln) = ln(40)
lnx + (-3ln + lnx) = ln(40)

Reorder the terms:
-3ln + lnx + lnx = ln(40)

Combine like terms: lnx + lnx = 2lnx
-3ln + 2lnx = ln(40)

Reorder the terms for easier multiplication:
-3ln + 2lnx = 40ln

Solving
-3ln + 2lnx = 40ln

Solving for variable 'l'.

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

Add '-40ln' to each side of the equation.
-3ln + -40ln + 2lnx = 40ln + -40ln

Combine like terms: -3ln + -40ln = -43ln
-43ln + 2lnx = 40ln + -40ln

Combine like terms: 40ln + -40ln = 0
-43ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-43 + 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 '(-43 + 2x)' equal to zero and attempt to solve:

Simplifying
-43 + 2x = 0

Solving
-43 + 2x = 0

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

Add '43' to each side of the equation.
-43 + 43 + 2x = 0 + 43

Combine like terms: -43 + 43 = 0
0 + 2x = 0 + 43
2x = 0 + 43

Combine like terms: 0 + 43 = 43
2x = 43

Add '-2x' to each side of the equation.
2x + -2x = 43 + -2x

Combine like terms: 2x + -2x = 0
0 = 43 + -2x

Simplifying
0 = 43 + -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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