log(6x+5)=log(x+4)+log(2)

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Solution for log(6x+5)=log(x+4)+log(2) equation:


Simplifying
log(6x + 5) = log(x + 4) + log(2)

Reorder the terms:
glo(5 + 6x) = log(x + 4) + log(2)
(5 * glo + 6x * glo) = log(x + 4) + log(2)
(5glo + 6glox) = log(x + 4) + log(2)

Reorder the terms:
5glo + 6glox = glo(4 + x) + log(2)
5glo + 6glox = (4 * glo + x * glo) + log(2)
5glo + 6glox = (4glo + glox) + log(2)

Reorder the terms for easier multiplication:
5glo + 6glox = 4glo + glox + 2glo

Reorder the terms:
5glo + 6glox = 4glo + 2glo + glox

Combine like terms: 4glo + 2glo = 6glo
5glo + 6glox = 6glo + glox

Solving
5glo + 6glox = 6glo + glox

Solving for variable 'g'.

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

Add '-6glo' to each side of the equation.
5glo + -6glo + 6glox = 6glo + -6glo + glox

Combine like terms: 5glo + -6glo = -1glo
-1glo + 6glox = 6glo + -6glo + glox

Combine like terms: 6glo + -6glo = 0
-1glo + 6glox = 0 + glox
-1glo + 6glox = glox

Add '-1glox' to each side of the equation.
-1glo + 6glox + -1glox = glox + -1glox

Combine like terms: 6glox + -1glox = 5glox
-1glo + 5glox = glox + -1glox

Combine like terms: glox + -1glox = 0
-1glo + 5glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-1 + 5x) = 0

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 '(-1 + 5x)' equal to zero and attempt to solve: Simplifying -1 + 5x = 0 Solving -1 + 5x = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5x = 0 + 1 5x = 0 + 1 Combine like terms: 0 + 1 = 1 5x = 1 Add '-5x' to each side of the equation. 5x + -5x = 1 + -5x Combine like terms: 5x + -5x = 0 0 = 1 + -5x Simplifying 0 = 1 + -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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