2+log[6](x-7)=log[6](22x)

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Solution for 2+log[6](x-7)=log[6](22x) equation:


Simplifying
2 + log[6](x + -7) = log[6](22x)

Reorder the terms:
2 + glo * 6(-7 + x) = log[6](22x)

Reorder the terms for easier multiplication:
2 + 6glo(-7 + x) = log[6](22x)
2 + (-7 * 6glo + x * 6glo) = log[6](22x)
2 + (-42glo + 6glox) = log[6](22x)

Remove parenthesis around (22x)
2 + -42glo + 6glox = glo * 6 * 22x

Reorder the terms for easier multiplication:
2 + -42glo + 6glox = 6 * 22glo * x

Multiply 6 * 22
2 + -42glo + 6glox = 132glo * x

Multiply glo * x
2 + -42glo + 6glox = 132glox

Solving
2 + -42glo + 6glox = 132glox

Solving for variable 'g'.

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

Add '-132glox' to each side of the equation.
2 + -42glo + 6glox + -132glox = 132glox + -132glox

Combine like terms: 6glox + -132glox = -126glox
2 + -42glo + -126glox = 132glox + -132glox

Combine like terms: 132glox + -132glox = 0
2 + -42glo + -126glox = 0

Add '-2' to each side of the equation.
2 + -42glo + -2 + -126glox = 0 + -2

Reorder the terms:
2 + -2 + -42glo + -126glox = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -42glo + -126glox = 0 + -2
-42glo + -126glox = 0 + -2

Combine like terms: 0 + -2 = -2
-42glo + -126glox = -2

Reorder the terms:
2 + -42glo + -126glox = -2 + 2

Combine like terms: -2 + 2 = 0
2 + -42glo + -126glox = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -21glo + -63glox) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + -21glo + -63glox)' equal to zero and attempt to solve: Simplifying 1 + -21glo + -63glox = 0 Solving 1 + -21glo + -63glox = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -21glo + -1 + -63glox = 0 + -1 Reorder the terms: 1 + -1 + -21glo + -63glox = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -21glo + -63glox = 0 + -1 -21glo + -63glox = 0 + -1 Combine like terms: 0 + -1 = -1 -21glo + -63glox = -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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