log(5x+7)=log(x-8)

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Solution for log(5x+7)=log(x-8) equation: 


Simplifying
log(5x + 7) = log(x + -8)

Reorder the terms:
glo(7 + 5x) = log(x + -8)
(7 * glo + 5x * glo) = log(x + -8)
(7glo + 5glox) = log(x + -8)

Reorder the terms:
7glo + 5glox = glo(-8 + x)
7glo + 5glox = (-8 * glo + x * glo)
7glo + 5glox = (-8glo + glox)

Solving
7glo + 5glox = -8glo + glox

Solving for variable 'g'.

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

Add '8glo' to each side of the equation.
7glo + 8glo + 5glox = -8glo + 8glo + glox

Combine like terms: 7glo + 8glo = 15glo
15glo + 5glox = -8glo + 8glo + glox

Combine like terms: -8glo + 8glo = 0
15glo + 5glox = 0 + glox
15glo + 5glox = glox

Add '-1glox' to each side of the equation.
15glo + 5glox + -1glox = glox + -1glox

Combine like terms: 5glox + -1glox = 4glox
15glo + 4glox = glox + -1glox

Combine like terms: glox + -1glox = 0
15glo + 4glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(15 + 4x) = 0


Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve:

Simplifying
glo = 0

Solving
glo = 0

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

Simplifying
glo = 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 + 4x)' equal to zero and attempt to solve:

Simplifying
15 + 4x = 0

Solving
15 + 4x = 0

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

Add '-15' to each side of the equation.
15 + -15 + 4x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 4x = 0 + -15
4x = 0 + -15

Combine like terms: 0 + -15 = -15
4x = -15

Add '-4x' to each side of the equation.
4x + -4x = -15 + -4x

Combine like terms: 4x + -4x = 0
0 = -15 + -4x

Simplifying
0 = -15 + -4x

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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