Log(x)+log(x+5)=log(6x+5)

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


Simplifying
Log(x) + log(x + 5) = log(6x + 5)

Multiply goL * x
goxL + log(x + 5) = log(6x + 5)

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

Reorder the terms:
5glo + glox + goxL = log(6x + 5)

Reorder the terms:
5glo + glox + goxL = glo(5 + 6x)
5glo + glox + goxL = (5 * glo + 6x * glo)
5glo + glox + goxL = (5glo + 6glox)

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

Reorder the terms:
5glo + -5glo + glox + goxL = 5glo + -5glo + 6glox

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

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

Solving
glox + goxL = 6glox

Solving for variable 'g'.

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

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

Combine like terms: glox + -6glox = -5glox
-5glox + goxL = 6glox + -6glox

Combine like terms: 6glox + -6glox = 0
-5glox + goxL = 0

Factor out the Greatest Common Factor (GCF), 'gox'.
gox(-5l + L) = 0

Subproblem 1

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