2log(x)=log(10-3x)

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Solution for 2log(x)=log(10-3x) equation: 


Simplifying
2log(x) = log(10 + -3x)

Multiply glo * x
2glox = log(10 + -3x)
2glox = (10 * glo + -3x * glo)
2glox = (10glo + -3glox)

Solving
2glox = 10glo + -3glox

Solving for variable 'g'.

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

Add '-10glo' to each side of the equation.
-10glo + 2glox = 10glo + -10glo + -3glox

Combine like terms: 10glo + -10glo = 0
-10glo + 2glox = 0 + -3glox
-10glo + 2glox = -3glox

Add '3glox' to each side of the equation.
-10glo + 2glox + 3glox = -3glox + 3glox

Combine like terms: 2glox + 3glox = 5glox
-10glo + 5glox = -3glox + 3glox

Combine like terms: -3glox + 3glox = 0
-10glo + 5glox = 0

Factor out the Greatest Common Factor (GCF), '5glo'.
5glo(-2 + x) = 0

Ignore the factor 5.

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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Add '-1x' to each side of the equation.
x + -1x = 2 + -1x

Combine like terms: x + -1x = 0
0 = 2 + -1x

Simplifying
0 = 2 + -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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