Log(3x)=log(5)+log(x+-4)

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


Simplifying
Log(3x) = log(5) + log(x + -4)

Remove parenthesis around (3x)
goL * 3x = log(5) + log(x + -4)

Reorder the terms for easier multiplication:
3goL * x = log(5) + log(x + -4)

Multiply goL * x
3goxL = log(5) + log(x + -4)

Reorder the terms for easier multiplication:
3goxL = 5glo + log(x + -4)

Reorder the terms:
3goxL = 5glo + glo(-4 + x)
3goxL = 5glo + (-4 * glo + x * glo)
3goxL = 5glo + (-4glo + glox)

Combine like terms: 5glo + -4glo = 1glo
3goxL = 1glo + glox

Solving
3goxL = 1glo + glox

Solving for variable 'g'.

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

Add '-1glo' to each side of the equation.
-1glo + 3goxL = 1glo + -1glo + glox

Combine like terms: 1glo + -1glo = 0
-1glo + 3goxL = 0 + glox
-1glo + 3goxL = glox

Add '-1glox' to each side of the equation.
-1glo + -1glox + 3goxL = glox + -1glox

Combine like terms: glox + -1glox = 0
-1glo + -1glox + 3goxL = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(-1l + -1lx + 3xL) = 0

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 '(-1l + -1lx + 3xL)' equal to zero and attempt to solve: Simplifying -1l + -1lx + 3xL = 0 Solving -1l + -1lx + 3xL = 0 Move all terms containing g to the left, all other terms to the right. Add 'l' to each side of the equation. -1l + -1lx + l + 3xL = 0 + l Reorder the terms: -1l + l + -1lx + 3xL = 0 + l Combine like terms: -1l + l = 0 0 + -1lx + 3xL = 0 + l -1lx + 3xL = 0 + l Remove the zero: -1lx + 3xL = l Add 'lx' to each side of the equation. -1lx + lx + 3xL = l + lx Combine like terms: -1lx + lx = 0 0 + 3xL = l + lx 3xL = l + lx Add '-3xL' to each side of the equation. 3xL + -3xL = l + lx + -3xL Combine like terms: 3xL + -3xL = 0 0 = l + lx + -3xL Simplifying 0 = l + lx + -3xL 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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