log(6)(x+53)+log(6)(x+3)=3

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Solution for log(6)(x+53)+log(6)(x+3)=3 equation:


Simplifying
log(6)(x + 53) + log(6)(x + 3) = 3

Reorder the terms:
glo * 6(53 + x) + log(6)(x + 3) = 3

Reorder the terms for easier multiplication:
6glo(53 + x) + log(6)(x + 3) = 3
(53 * 6glo + x * 6glo) + log(6)(x + 3) = 3
(318glo + 6glox) + log(6)(x + 3) = 3

Reorder the terms:
318glo + 6glox + glo * 6(3 + x) = 3

Reorder the terms for easier multiplication:
318glo + 6glox + 6glo(3 + x) = 3
318glo + 6glox + (3 * 6glo + x * 6glo) = 3
318glo + 6glox + (18glo + 6glox) = 3

Reorder the terms:
318glo + 18glo + 6glox + 6glox = 3

Combine like terms: 318glo + 18glo = 336glo
336glo + 6glox + 6glox = 3

Combine like terms: 6glox + 6glox = 12glox
336glo + 12glox = 3

Solving
336glo + 12glox = 3

Solving for variable 'g'.

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

Reorder the terms:
-3 + 336glo + 12glox = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 336glo + 12glox = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 112glo + 4glox) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + 112glo + 4glox)' equal to zero and attempt to solve: Simplifying -1 + 112glo + 4glox = 0 Solving -1 + 112glo + 4glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 112glo + 1 + 4glox = 0 + 1 Reorder the terms: -1 + 1 + 112glo + 4glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 112glo + 4glox = 0 + 1 112glo + 4glox = 0 + 1 Combine like terms: 0 + 1 = 1 112glo + 4glox = 1 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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