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

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


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

Reorder the terms:
2glo(2 + x) = log(3x + 10)
(2 * 2glo + x * 2glo) = log(3x + 10)
(4glo + 2glox) = log(3x + 10)

Reorder the terms:
4glo + 2glox = glo(10 + 3x)
4glo + 2glox = (10 * glo + 3x * glo)
4glo + 2glox = (10glo + 3glox)

Solving
4glo + 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.
4glo + -10glo + 2glox = 10glo + -10glo + 3glox

Combine like terms: 4glo + -10glo = -6glo
-6glo + 2glox = 10glo + -10glo + 3glox

Combine like terms: 10glo + -10glo = 0
-6glo + 2glox = 0 + 3glox
-6glo + 2glox = 3glox

Add '-3glox' to each side of the equation.
-6glo + 2glox + -3glox = 3glox + -3glox

Combine like terms: 2glox + -3glox = -1glox
-6glo + -1glox = 3glox + -3glox

Combine like terms: 3glox + -3glox = 0
-6glo + -1glox = 0

Factor out the Greatest Common Factor (GCF), '-1glo'.
-1glo(6 + x) = 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 '(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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