logx+log(x-16)=log(8x)

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Solution for logx+log(x-16)=log(8x) equation:


Simplifying
logx + log(x + -16) = log(8x)

Reorder the terms:
glox + glo(-16 + x) = log(8x)
glox + (-16 * glo + x * glo) = log(8x)
glox + (-16glo + glox) = log(8x)

Reorder the terms:
-16glo + glox + glox = log(8x)

Combine like terms: glox + glox = 2glox
-16glo + 2glox = log(8x)

Remove parenthesis around (8x)
-16glo + 2glox = glo * 8x

Reorder the terms for easier multiplication:
-16glo + 2glox = 8glo * x

Multiply glo * x
-16glo + 2glox = 8glox

Solving
-16glo + 2glox = 8glox

Solving for variable 'g'.

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

Add '-8glox' to each side of the equation.
-16glo + 2glox + -8glox = 8glox + -8glox

Combine like terms: 2glox + -8glox = -6glox
-16glo + -6glox = 8glox + -8glox

Combine like terms: 8glox + -8glox = 0
-16glo + -6glox = 0

Factor out the Greatest Common Factor (GCF), '-2glo'.
-2glo(8 + 3x) = 0

Ignore the factor -2.

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 '(8 + 3x)' equal to zero and attempt to solve: Simplifying 8 + 3x = 0 Solving 8 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3x = 0 + -8 3x = 0 + -8 Combine like terms: 0 + -8 = -8 3x = -8 Add '-3x' to each side of the equation. 3x + -3x = -8 + -3x Combine like terms: 3x + -3x = 0 0 = -8 + -3x Simplifying 0 = -8 + -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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