2lgx=lg(10-3x)

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


Simplifying
2lgx = lg(10 + -3x)
2glx = (10 * gl + -3x * gl)
2glx = (10gl + -3glx)

Solving
2glx = 10gl + -3glx

Solving for variable 'g'.

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

Add '-10gl' to each side of the equation.
-10gl + 2glx = 10gl + -10gl + -3glx

Combine like terms: 10gl + -10gl = 0
-10gl + 2glx = 0 + -3glx
-10gl + 2glx = -3glx

Add '3glx' to each side of the equation.
-10gl + 2glx + 3glx = -3glx + 3glx

Combine like terms: 2glx + 3glx = 5glx
-10gl + 5glx = -3glx + 3glx

Combine like terms: -3glx + 3glx = 0
-10gl + 5glx = 0

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

Ignore the factor 5.

Subproblem 1
Set the factor 'gl' equal to zero and attempt to solve:

Simplifying
gl = 0

Solving
gl = 0

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

Simplifying
gl = 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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