log(4x+21)=logx+log(x+8)

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Solution for log(4x+21)=logx+log(x+8) equation:


Simplifying
log(4x + 21) = logx + log(x + 8)

Reorder the terms:
glo(21 + 4x) = logx + log(x + 8)
(21 * glo + 4x * glo) = logx + log(x + 8)
(21glo + 4glox) = logx + log(x + 8)

Reorder the terms:
21glo + 4glox = glox + glo(8 + x)
21glo + 4glox = glox + (8 * glo + x * glo)
21glo + 4glox = glox + (8glo + glox)

Reorder the terms:
21glo + 4glox = 8glo + glox + glox

Combine like terms: glox + glox = 2glox
21glo + 4glox = 8glo + 2glox

Solving
21glo + 4glox = 8glo + 2glox

Solving for variable 'g'.

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

Add '-8glo' to each side of the equation.
21glo + -8glo + 4glox = 8glo + -8glo + 2glox

Combine like terms: 21glo + -8glo = 13glo
13glo + 4glox = 8glo + -8glo + 2glox

Combine like terms: 8glo + -8glo = 0
13glo + 4glox = 0 + 2glox
13glo + 4glox = 2glox

Add '-2glox' to each side of the equation.
13glo + 4glox + -2glox = 2glox + -2glox

Combine like terms: 4glox + -2glox = 2glox
13glo + 2glox = 2glox + -2glox

Combine like terms: 2glox + -2glox = 0
13glo + 2glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(13 + 2x) = 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 '(13 + 2x)' equal to zero and attempt to solve: Simplifying 13 + 2x = 0 Solving 13 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 2x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 2x = 0 + -13 2x = 0 + -13 Combine like terms: 0 + -13 = -13 2x = -13 Add '-2x' to each side of the equation. 2x + -2x = -13 + -2x Combine like terms: 2x + -2x = 0 0 = -13 + -2x Simplifying 0 = -13 + -2x 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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