ln(x-7)+ln(x)=ln(8)

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Solution for ln(x-7)+ln(x)=ln(8) equation: 


Simplifying
ln(x + -7) + ln(x) = ln(8)

Reorder the terms:
ln(-7 + x) + ln(x) = ln(8)
(-7 * ln + x * ln) + ln(x) = ln(8)
(-7ln + lnx) + ln(x) = ln(8)

Multiply ln * x
-7ln + lnx + lnx = ln(8)

Combine like terms: lnx + lnx = 2lnx
-7ln + 2lnx = ln(8)

Reorder the terms for easier multiplication:
-7ln + 2lnx = 8ln

Solving
-7ln + 2lnx = 8ln

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
-7ln + -8ln + 2lnx = 8ln + -8ln

Combine like terms: -7ln + -8ln = -15ln
-15ln + 2lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-15ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-15 + 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 '(-15 + 2x)' equal to zero and attempt to solve:

Simplifying
-15 + 2x = 0

Solving
-15 + 2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + 2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 2x = 0 + 15
2x = 0 + 15

Combine like terms: 0 + 15 = 15
2x = 15

Add '-2x' to each side of the equation.
2x + -2x = 15 + -2x

Combine like terms: 2x + -2x = 0
0 = 15 + -2x

Simplifying
0 = 15 + -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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