-log(2x+3)-4log(x)=log(x)

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Solution for -log(2x+3)-4log(x)=log(x) equation: 


Simplifying
-1log(2x + 3) + -4log(x) = log(x)

Reorder the terms:
-1glo(3 + 2x) + -4log(x) = log(x)
(3 * -1glo + 2x * -1glo) + -4log(x) = log(x)
(-3glo + -2glox) + -4log(x) = log(x)

Multiply glo * x
-3glo + -2glox + -4glox = log(x)

Combine like terms: -2glox + -4glox = -6glox
-3glo + -6glox = log(x)

Multiply glo * x
-3glo + -6glox = glox

Solving
-3glo + -6glox = glox

Solving for variable 'g'.

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

Add '-1glox' to each side of the equation.
-3glo + -6glox + -1glox = glox + -1glox

Combine like terms: -6glox + -1glox = -7glox
-3glo + -7glox = glox + -1glox

Combine like terms: glox + -1glox = 0
-3glo + -7glox = 0

Factor out the Greatest Common Factor (GCF), '-1glo'.
-1glo(3 + 7x) = 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 '(3 + 7x)' equal to zero and attempt to solve:

Simplifying
3 + 7x = 0

Solving
3 + 7x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7x = 0 + -3
7x = 0 + -3

Combine like terms: 0 + -3 = -3
7x = -3

Add '-7x' to each side of the equation.
7x + -7x = -3 + -7x

Combine like terms: 7x + -7x = 0
0 = -3 + -7x

Simplifying
0 = -3 + -7x

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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