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

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


Simplifying
log(x + 7) + -1log(x + -2) = logx

Reorder the terms:
glo(7 + x) + -1log(x + -2) = logx
(7 * glo + x * glo) + -1log(x + -2) = logx
(7glo + glox) + -1log(x + -2) = logx

Reorder the terms:
7glo + glox + -1glo(-2 + x) = logx
7glo + glox + (-2 * -1glo + x * -1glo) = logx
7glo + glox + (2glo + -1glox) = logx

Reorder the terms:
7glo + 2glo + glox + -1glox = logx

Combine like terms: 7glo + 2glo = 9glo
9glo + glox + -1glox = logx

Combine like terms: glox + -1glox = 0
9glo + 0 = logx
9glo = logx

Solving
9glo = glox

Solving for variable 'g'.

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

Add '-1glox' to each side of the equation.
9glo + -1glox = glox + -1glox

Combine like terms: glox + -1glox = 0
9glo + -1glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(9 + -1x) = 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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Add 'x' to each side of the equation.
-1x + x = -9 + x

Combine like terms: -1x + x = 0
0 = -9 + x

Simplifying
0 = -9 + x

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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