2lgx=lg(x+6)

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Solution for 2lgx=lg(x+6) equation:


Simplifying
2lgx = lg(x + 6)

Reorder the terms:
2glx = gl(6 + x)
2glx = (6 * gl + x * gl)
2glx = (6gl + glx)

Solving
2glx = 6gl + glx

Solving for variable 'g'.

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

Add '-6gl' to each side of the equation.
-6gl + 2glx = 6gl + -6gl + glx

Combine like terms: 6gl + -6gl = 0
-6gl + 2glx = 0 + glx
-6gl + 2glx = glx

Add '-1glx' to each side of the equation.
-6gl + 2glx + -1glx = glx + -1glx

Combine like terms: 2glx + -1glx = 1glx
-6gl + 1glx = glx + -1glx

Combine like terms: glx + -1glx = 0
-6gl + 1glx = 0

Factor out the Greatest Common Factor (GCF), 'gl'.
gl(-6 + x) = 0

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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -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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