log(x)+log(x-19)=log(19x)

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Solution for log(x)+log(x-19)=log(19x) equation:


Simplifying
log(x) + log(x + -19) = log(19x)

Multiply glo * x
glox + log(x + -19) = log(19x)

Reorder the terms:
glox + glo(-19 + x) = log(19x)
glox + (-19 * glo + x * glo) = log(19x)
glox + (-19glo + glox) = log(19x)

Reorder the terms:
-19glo + glox + glox = log(19x)

Combine like terms: glox + glox = 2glox
-19glo + 2glox = log(19x)

Remove parenthesis around (19x)
-19glo + 2glox = glo * 19x

Reorder the terms for easier multiplication:
-19glo + 2glox = 19glo * x

Multiply glo * x
-19glo + 2glox = 19glox

Solving
-19glo + 2glox = 19glox

Solving for variable 'g'.

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

Add '-19glox' to each side of the equation.
-19glo + 2glox + -19glox = 19glox + -19glox

Combine like terms: 2glox + -19glox = -17glox
-19glo + -17glox = 19glox + -19glox

Combine like terms: 19glox + -19glox = 0
-19glo + -17glox = 0

Factor out the Greatest Common Factor (GCF), '-1glo'.
-1glo(19 + 17x) = 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 + 17x)' equal to zero and attempt to solve: Simplifying 19 + 17x = 0 Solving 19 + 17x = 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 + 17x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 17x = 0 + -19 17x = 0 + -19 Combine like terms: 0 + -19 = -19 17x = -19 Add '-17x' to each side of the equation. 17x + -17x = -19 + -17x Combine like terms: 17x + -17x = 0 0 = -19 + -17x Simplifying 0 = -19 + -17x 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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