logx+log(4x-7)=log(6x+12)

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Solution for logx+log(4x-7)=log(6x+12) equation:


Simplifying
logx + log(4x + -7) = log(6x + 12)

Reorder the terms:
glox + glo(-7 + 4x) = log(6x + 12)
glox + (-7 * glo + 4x * glo) = log(6x + 12)
glox + (-7glo + 4glox) = log(6x + 12)

Reorder the terms:
-7glo + glox + 4glox = log(6x + 12)

Combine like terms: glox + 4glox = 5glox
-7glo + 5glox = log(6x + 12)

Reorder the terms:
-7glo + 5glox = glo(12 + 6x)
-7glo + 5glox = (12 * glo + 6x * glo)
-7glo + 5glox = (12glo + 6glox)

Solving
-7glo + 5glox = 12glo + 6glox

Solving for variable 'g'.

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

Add '-12glo' to each side of the equation.
-7glo + -12glo + 5glox = 12glo + -12glo + 6glox

Combine like terms: -7glo + -12glo = -19glo
-19glo + 5glox = 12glo + -12glo + 6glox

Combine like terms: 12glo + -12glo = 0
-19glo + 5glox = 0 + 6glox
-19glo + 5glox = 6glox

Add '-6glox' to each side of the equation.
-19glo + 5glox + -6glox = 6glox + -6glox

Combine like terms: 5glox + -6glox = -1glox
-19glo + -1glox = 6glox + -6glox

Combine like terms: 6glox + -6glox = 0
-19glo + -1glox = 0

Factor out the Greatest Common Factor (GCF), '-1glo'.
-1glo(19 + x) = 0

Ignore the factor -1.

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 '(19 + x)' equal to zero and attempt to solve: Simplifying 19 + x = 0 Solving 19 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + x = 0 + -19 x = 0 + -19 Combine like terms: 0 + -19 = -19 x = -19 Add '-1x' to each side of the equation. x + -1x = -19 + -1x Combine like terms: x + -1x = 0 0 = -19 + -1x Simplifying 0 = -19 + -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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