log(w^2+21)=log(10w)

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Solution for log(w^2+21)=log(10w) equation: 


Simplifying
log(w2 + 21) = log(10w)

Reorder the terms:
glo(21 + w2) = log(10w)
(21 * glo + w2 * glo) = log(10w)
(21glo + glow2) = log(10w)

Remove parenthesis around (10w)
21glo + glow2 = glo * 10w

Reorder the terms for easier multiplication:
21glo + glow2 = 10glo * w

Multiply glo * w
21glo + glow2 = 10glow

Solving
21glo + glow2 = 10glow

Solving for variable 'g'.

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

Add '-10glow' to each side of the equation.
21glo + -10glow + glow2 = 10glow + -10glow

Combine like terms: 10glow + -10glow = 0
21glo + -10glow + glow2 = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(21 + -10w + w2) = 0

Factor a trinomial.
glo((3 + -1w)(7 + -1w)) = 0


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 '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Add 'w' to each side of the equation.
-1w + w = -3 + w

Combine like terms: -1w + w = 0
0 = -3 + w

Simplifying
0 = -3 + w

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Add 'w' to each side of the equation.
-1w + w = -7 + w

Combine like terms: -1w + w = 0
0 = -7 + w

Simplifying
0 = -7 + w

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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