2log(x+5)=log(x-7)

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Solution for 2log(x+5)=log(x-7) equation: 


Simplifying
2log(x + 5) = log(x + -7)

Reorder the terms:
2glo(5 + x) = log(x + -7)
(5 * 2glo + x * 2glo) = log(x + -7)
(10glo + 2glox) = log(x + -7)

Reorder the terms:
10glo + 2glox = glo(-7 + x)
10glo + 2glox = (-7 * glo + x * glo)
10glo + 2glox = (-7glo + glox)

Solving
10glo + 2glox = -7glo + glox

Solving for variable 'g'.

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

Add '7glo' to each side of the equation.
10glo + 7glo + 2glox = -7glo + 7glo + glox

Combine like terms: 10glo + 7glo = 17glo
17glo + 2glox = -7glo + 7glo + glox

Combine like terms: -7glo + 7glo = 0
17glo + 2glox = 0 + glox
17glo + 2glox = glox

Add '-1glox' to each side of the equation.
17glo + 2glox + -1glox = glox + -1glox

Combine like terms: 2glox + -1glox = 1glox
17glo + 1glox = glox + -1glox

Combine like terms: glox + -1glox = 0
17glo + 1glox = 0

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

Simplifying
17 + x = 0

Solving
17 + x = 0

Move all terms containing g 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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