Log[5](x-7)=log[5](x-3)+1

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Solution for Log[5](x-7)=log[5](x-3)+1 equation: 


Simplifying
Log[5](x + -7) = log[5](x + -3) + 1

Reorder the terms:
goL * 5(-7 + x) = log[5](x + -3) + 1

Reorder the terms for easier multiplication:
5goL(-7 + x) = log[5](x + -3) + 1
(-7 * 5goL + x * 5goL) = log[5](x + -3) + 1
(-35goL + 5goxL) = log[5](x + -3) + 1

Reorder the terms:
-35goL + 5goxL = glo * 5(-3 + x) + 1

Reorder the terms for easier multiplication:
-35goL + 5goxL = 5glo(-3 + x) + 1
-35goL + 5goxL = (-3 * 5glo + x * 5glo) + 1
-35goL + 5goxL = (-15glo + 5glox) + 1

Reorder the terms:
-35goL + 5goxL = 1 + -15glo + 5glox

Solving
-35goL + 5goxL = 1 + -15glo + 5glox

Solving for variable 'g'.

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

Add '15glo' to each side of the equation.
-35goL + 15glo + 5goxL = 1 + -15glo + 15glo + 5glox

Reorder the terms:
15glo + -35goL + 5goxL = 1 + -15glo + 15glo + 5glox

Combine like terms: -15glo + 15glo = 0
15glo + -35goL + 5goxL = 1 + 0 + 5glox
15glo + -35goL + 5goxL = 1 + 5glox

Add '-5glox' to each side of the equation.
15glo + -35goL + -5glox + 5goxL = 1 + 5glox + -5glox

Reorder the terms:
15glo + -5glox + -35goL + 5goxL = 1 + 5glox + -5glox

Combine like terms: 5glox + -5glox = 0
15glo + -5glox + -35goL + 5goxL = 1 + 0
15glo + -5glox + -35goL + 5goxL = 1

Reorder the terms:
-1 + 15glo + -5glox + -35goL + 5goxL = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 15glo + -5glox + -35goL + 5goxL = 0

The solution to this equation could not be determined.

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