Log(4)(3x)=log(4)35-log(4)3+log(4)7

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Solution for Log(4)(3x)=log(4)35-log(4)3+log(4)7 equation:


Simplifying
Log(4)(3x) = log(4) * 35 + -1log(4) * 3 + log(4) * 7

Remove parenthesis around (3x)
goL * 4 * 3x = log(4) * 35 + -1log(4) * 3 + log(4) * 7

Reorder the terms for easier multiplication:
4 * 3goL * x = log(4) * 35 + -1log(4) * 3 + log(4) * 7

Multiply 4 * 3
12goL * x = log(4) * 35 + -1log(4) * 3 + log(4) * 7

Multiply goL * x
12goxL = log(4) * 35 + -1log(4) * 3 + log(4) * 7

Reorder the terms for easier multiplication:
12goxL = 4 * 35glo + -1log(4) * 3 + log(4) * 7

Multiply 4 * 35
12goxL = 140glo + -1log(4) * 3 + log(4) * 7

Reorder the terms for easier multiplication:
12goxL = 140glo + -1 * 4 * 3glo + log(4) * 7

Multiply -1 * 4
12goxL = 140glo + -4 * 3glo + log(4) * 7

Multiply -4 * 3
12goxL = 140glo + -12glo + log(4) * 7

Reorder the terms for easier multiplication:
12goxL = 140glo + -12glo + 4 * 7glo

Multiply 4 * 7
12goxL = 140glo + -12glo + 28glo

Combine like terms: 140glo + -12glo = 128glo
12goxL = 128glo + 28glo

Combine like terms: 128glo + 28glo = 156glo
12goxL = 156glo

Solving
12goxL = 156glo

Solving for variable 'g'.

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

Add '-156glo' to each side of the equation.
-156glo + 12goxL = 156glo + -156glo

Combine like terms: 156glo + -156glo = 0
-156glo + 12goxL = 0

Factor out the Greatest Common Factor (GCF), '12go'.
12go(-13l + xL) = 0

Ignore the factor 12.

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 '(-13l + xL)' equal to zero and attempt to solve: Simplifying -13l + xL = 0 Solving -13l + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '13l' to each side of the equation. -13l + 13l + xL = 0 + 13l Combine like terms: -13l + 13l = 0 0 + xL = 0 + 13l xL = 0 + 13l Remove the zero: xL = 13l Add '-1xL' to each side of the equation. xL + -1xL = 13l + -1xL Combine like terms: xL + -1xL = 0 0 = 13l + -1xL Simplifying 0 = 13l + -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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