-2lg(x)+3lg(x^2)=lg(27x)

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Solution for -2lg(x)+3lg(x^2)=lg(27x) equation: 


Simplifying
-2lg(x) + 3lg(x2) = lg(27x)

Multiply gl * x
-2glx + 3lg(x2) = lg(27x)

Multiply gl * x2
-2glx + 3glx2 = lg(27x)

Remove parenthesis around (27x)
-2glx + 3glx2 = gl * 27x

Reorder the terms for easier multiplication:
-2glx + 3glx2 = 27gl * x

Multiply gl * x
-2glx + 3glx2 = 27glx

Solving
-2glx + 3glx2 = 27glx

Solving for variable 'g'.

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

Add '-27glx' to each side of the equation.
-2glx + -27glx + 3glx2 = 27glx + -27glx

Combine like terms: -2glx + -27glx = -29glx
-29glx + 3glx2 = 27glx + -27glx

Combine like terms: 27glx + -27glx = 0
-29glx + 3glx2 = 0

Factor out the Greatest Common Factor (GCF), 'glx'.
glx(-29 + 3x) = 0


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

Simplifying
glx = 0

Solving
glx = 0

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

Simplifying
glx = 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 '(-29 + 3x)' equal to zero and attempt to solve:

Simplifying
-29 + 3x = 0

Solving
-29 + 3x = 0

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

Add '29' to each side of the equation.
-29 + 29 + 3x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 3x = 0 + 29
3x = 0 + 29

Combine like terms: 0 + 29 = 29
3x = 29

Add '-3x' to each side of the equation.
3x + -3x = 29 + -3x

Combine like terms: 3x + -3x = 0
0 = 29 + -3x

Simplifying
0 = 29 + -3x

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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