log[5](x+4)=1-log[5](x+8)

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Solution for log[5](x+4)=1-log[5](x+8) equation: 


Simplifying
log[5](x + 4) = 1 + -1log[5](x + 8)

Reorder the terms:
glo * 5(4 + x) = 1 + -1log[5](x + 8)

Reorder the terms for easier multiplication:
5glo(4 + x) = 1 + -1log[5](x + 8)
(4 * 5glo + x * 5glo) = 1 + -1log[5](x + 8)
(20glo + 5glox) = 1 + -1log[5](x + 8)

Reorder the terms:
20glo + 5glox = 1 + -1glo * 5(8 + x)

Reorder the terms for easier multiplication:
20glo + 5glox = 1 + -1 * 5glo(8 + x)

Multiply -1 * 5
20glo + 5glox = 1 + -5glo(8 + x)
20glo + 5glox = 1 + (8 * -5glo + x * -5glo)
20glo + 5glox = 1 + (-40glo + -5glox)

Solving
20glo + 5glox = 1 + -40glo + -5glox

Solving for variable 'g'.

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

Add '40glo' to each side of the equation.
20glo + 40glo + 5glox = 1 + -40glo + 40glo + -5glox

Combine like terms: 20glo + 40glo = 60glo
60glo + 5glox = 1 + -40glo + 40glo + -5glox

Combine like terms: -40glo + 40glo = 0
60glo + 5glox = 1 + 0 + -5glox
60glo + 5glox = 1 + -5glox

Add '5glox' to each side of the equation.
60glo + 5glox + 5glox = 1 + -5glox + 5glox

Combine like terms: 5glox + 5glox = 10glox
60glo + 10glox = 1 + -5glox + 5glox

Combine like terms: -5glox + 5glox = 0
60glo + 10glox = 1 + 0
60glo + 10glox = 1

Reorder the terms:
-1 + 60glo + 10glox = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 60glo + 10glox = 0

The solution to this equation could not be determined.

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