log(4)(3x-5)=log(4)11+log(4)2

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Solution for log(4)(3x-5)=log(4)11+log(4)2 equation:


Simplifying
log(4)(3x + -5) = log(4) * 11 + log(4) * 2

Reorder the terms:
glo * 4(-5 + 3x) = log(4) * 11 + log(4) * 2

Reorder the terms for easier multiplication:
4glo(-5 + 3x) = log(4) * 11 + log(4) * 2
(-5 * 4glo + 3x * 4glo) = log(4) * 11 + log(4) * 2
(-20glo + 12glox) = log(4) * 11 + log(4) * 2

Reorder the terms for easier multiplication:
-20glo + 12glox = 4 * 11glo + log(4) * 2

Multiply 4 * 11
-20glo + 12glox = 44glo + log(4) * 2

Reorder the terms for easier multiplication:
-20glo + 12glox = 44glo + 4 * 2glo

Multiply 4 * 2
-20glo + 12glox = 44glo + 8glo

Combine like terms: 44glo + 8glo = 52glo
-20glo + 12glox = 52glo

Solving
-20glo + 12glox = 52glo

Solving for variable 'g'.

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

Add '-52glo' to each side of the equation.
-20glo + -52glo + 12glox = 52glo + -52glo

Combine like terms: -20glo + -52glo = -72glo
-72glo + 12glox = 52glo + -52glo

Combine like terms: 52glo + -52glo = 0
-72glo + 12glox = 0

Factor out the Greatest Common Factor (GCF), '12glo'.
12glo(-6 + x) = 0

Ignore the factor 12.

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