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

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


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

Multiply goL * x
goxL + log(x + 3) = log(10)

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

Reorder the terms:
3glo + glox + goxL = log(10)

Reorder the terms for easier multiplication:
3glo + glox + goxL = 10glo

Solving
3glo + glox + goxL = 10glo

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.
3glo + glox + -10glo + goxL = 10glo + -10glo

Reorder the terms:
3glo + -10glo + glox + goxL = 10glo + -10glo

Combine like terms: 3glo + -10glo = -7glo
-7glo + glox + goxL = 10glo + -10glo

Combine like terms: 10glo + -10glo = 0
-7glo + glox + goxL = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(-7l + lx + xL) = 0

Subproblem 1

Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(-7l + lx + xL)' equal to zero and attempt to solve: Simplifying -7l + lx + xL = 0 Solving -7l + lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '7l' to each side of the equation. -7l + lx + 7l + xL = 0 + 7l Reorder the terms: -7l + 7l + lx + xL = 0 + 7l Combine like terms: -7l + 7l = 0 0 + lx + xL = 0 + 7l lx + xL = 0 + 7l Remove the zero: lx + xL = 7l Add '-1lx' to each side of the equation. lx + -1lx + xL = 7l + -1lx Combine like terms: lx + -1lx = 0 0 + xL = 7l + -1lx xL = 7l + -1lx Add '-1xL' to each side of the equation. xL + -1xL = 7l + -1lx + -1xL Combine like terms: xL + -1xL = 0 0 = 7l + -1lx + -1xL Simplifying 0 = 7l + -1lx + -1xL 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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