log[4](7x-6)=log[4](2x+8)

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Solution for log[4](7x-6)=log[4](2x+8) equation:


Simplifying
log[4](7x + -6) = log[4](2x + 8)

Reorder the terms:
glo * 4(-6 + 7x) = log[4](2x + 8)

Reorder the terms for easier multiplication:
4glo(-6 + 7x) = log[4](2x + 8)
(-6 * 4glo + 7x * 4glo) = log[4](2x + 8)
(-24glo + 28glox) = log[4](2x + 8)

Reorder the terms:
-24glo + 28glox = glo * 4(8 + 2x)

Reorder the terms for easier multiplication:
-24glo + 28glox = 4glo(8 + 2x)
-24glo + 28glox = (8 * 4glo + 2x * 4glo)
-24glo + 28glox = (32glo + 8glox)

Solving
-24glo + 28glox = 32glo + 8glox

Solving for variable 'g'.

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

Add '-32glo' to each side of the equation.
-24glo + -32glo + 28glox = 32glo + -32glo + 8glox

Combine like terms: -24glo + -32glo = -56glo
-56glo + 28glox = 32glo + -32glo + 8glox

Combine like terms: 32glo + -32glo = 0
-56glo + 28glox = 0 + 8glox
-56glo + 28glox = 8glox

Add '-8glox' to each side of the equation.
-56glo + 28glox + -8glox = 8glox + -8glox

Combine like terms: 28glox + -8glox = 20glox
-56glo + 20glox = 8glox + -8glox

Combine like terms: 8glox + -8glox = 0
-56glo + 20glox = 0

Factor out the Greatest Common Factor (GCF), '4glo'.
4glo(-14 + 5x) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(-14 + 5x)' equal to zero and attempt to solve: Simplifying -14 + 5x = 0 Solving -14 + 5x = 0 Move all terms containing g to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + 5x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 5x = 0 + 14 5x = 0 + 14 Combine like terms: 0 + 14 = 14 5x = 14 Add '-5x' to each side of the equation. 5x + -5x = 14 + -5x Combine like terms: 5x + -5x = 0 0 = 14 + -5x Simplifying 0 = 14 + -5x 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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