Log(81)(x+20)=log(81)(6x)

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Solution for Log(81)(x+20)=log(81)(6x) equation:


Simplifying
Log(81)(x + 20) = log(81)(6x)

Reorder the terms:
goL * 81(20 + x) = log(81)(6x)

Reorder the terms for easier multiplication:
81goL(20 + x) = log(81)(6x)
(20 * 81goL + x * 81goL) = log(81)(6x)
(1620goL + 81goxL) = log(81)(6x)

Remove parenthesis around (6x)
1620goL + 81goxL = glo * 81 * 6x

Reorder the terms for easier multiplication:
1620goL + 81goxL = 81 * 6glo * x

Multiply 81 * 6
1620goL + 81goxL = 486glo * x

Multiply glo * x
1620goL + 81goxL = 486glox

Solving
1620goL + 81goxL = 486glox

Solving for variable 'g'.

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

Add '-486glox' to each side of the equation.
1620goL + -486glox + 81goxL = 486glox + -486glox

Reorder the terms:
-486glox + 1620goL + 81goxL = 486glox + -486glox

Combine like terms: 486glox + -486glox = 0
-486glox + 1620goL + 81goxL = 0

Factor out the Greatest Common Factor (GCF), '81go'.
81go(-6lx + 20L + xL) = 0

Ignore the factor 81.

Subproblem 1

Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-6lx + 20L + xL)' equal to zero and attempt to solve: Simplifying -6lx + 20L + xL = 0 Reorder the terms: 20L + -6lx + xL = 0 Solving 20L + -6lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-20L' to each side of the equation. 20L + -6lx + -20L + xL = 0 + -20L Reorder the terms: 20L + -20L + -6lx + xL = 0 + -20L Combine like terms: 20L + -20L = 0 0 + -6lx + xL = 0 + -20L -6lx + xL = 0 + -20L Remove the zero: -6lx + xL = -20L Add '6lx' to each side of the equation. -6lx + 6lx + xL = -20L + 6lx Combine like terms: -6lx + 6lx = 0 0 + xL = -20L + 6lx xL = -20L + 6lx Add '-1xL' to each side of the equation. xL + -1xL = -20L + 6lx + -1xL Combine like terms: xL + -1xL = 0 0 = -20L + 6lx + -1xL Simplifying 0 = -20L + 6lx + -1xL 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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