Logbase(6)(x-6)=3-logbase(6)x

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Solution for Logbase(6)(x-6)=3-logbase(6)x equation:


Simplifying
Logbase(6)(x + -6) = 3 + -1logbase(6) * x

Reorder the terms:
abegosL * 6(-6 + x) = 3 + -1logbase(6) * x

Reorder the terms for easier multiplication:
6abegosL(-6 + x) = 3 + -1logbase(6) * x
(-6 * 6abegosL + x * 6abegosL) = 3 + -1logbase(6) * x
(-36abegosL + 6abegosxL) = 3 + -1logbase(6) * x

Reorder the terms for easier multiplication:
-36abegosL + 6abegosxL = 3 + -1 * 6abeglos * x

Multiply -1 * 6
-36abegosL + 6abegosxL = 3 + -6abeglos * x

Multiply abeglos * x
-36abegosL + 6abegosxL = 3 + -6abeglosx

Solving
-36abegosL + 6abegosxL = 3 + -6abeglosx

Solving for variable 'a'.

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

Add '6abeglosx' to each side of the equation.
-36abegosL + 6abeglosx + 6abegosxL = 3 + -6abeglosx + 6abeglosx

Reorder the terms:
6abeglosx + -36abegosL + 6abegosxL = 3 + -6abeglosx + 6abeglosx

Combine like terms: -6abeglosx + 6abeglosx = 0
6abeglosx + -36abegosL + 6abegosxL = 3 + 0
6abeglosx + -36abegosL + 6abegosxL = 3

Reorder the terms:
-3 + 6abeglosx + -36abegosL + 6abegosxL = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 6abeglosx + -36abegosL + 6abegosxL = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 2abeglosx + -12abegosL + 2abegosxL) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + 2abeglosx + -12abegosL + 2abegosxL)' equal to zero and attempt to solve: Simplifying -1 + 2abeglosx + -12abegosL + 2abegosxL = 0 Solving -1 + 2abeglosx + -12abegosL + 2abegosxL = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 2abeglosx + -12abegosL + 1 + 2abegosxL = 0 + 1 Reorder the terms: -1 + 1 + 2abeglosx + -12abegosL + 2abegosxL = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2abeglosx + -12abegosL + 2abegosxL = 0 + 1 2abeglosx + -12abegosL + 2abegosxL = 0 + 1 Combine like terms: 0 + 1 = 1 2abeglosx + -12abegosL + 2abegosxL = 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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