log(5x+3)+log(2)=log(9x+10)

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Solution for log(5x+3)+log(2)=log(9x+10) equation:


Simplifying
log(5x + 3) + log(2) = log(9x + 10)

Reorder the terms:
glo(3 + 5x) + log(2) = log(9x + 10)
(3 * glo + 5x * glo) + log(2) = log(9x + 10)
(3glo + 5glox) + log(2) = log(9x + 10)

Reorder the terms for easier multiplication:
3glo + 5glox + 2glo = log(9x + 10)

Reorder the terms:
3glo + 2glo + 5glox = log(9x + 10)

Combine like terms: 3glo + 2glo = 5glo
5glo + 5glox = log(9x + 10)

Reorder the terms:
5glo + 5glox = glo(10 + 9x)
5glo + 5glox = (10 * glo + 9x * glo)
5glo + 5glox = (10glo + 9glox)

Solving
5glo + 5glox = 10glo + 9glox

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.
5glo + -10glo + 5glox = 10glo + -10glo + 9glox

Combine like terms: 5glo + -10glo = -5glo
-5glo + 5glox = 10glo + -10glo + 9glox

Combine like terms: 10glo + -10glo = 0
-5glo + 5glox = 0 + 9glox
-5glo + 5glox = 9glox

Add '-9glox' to each side of the equation.
-5glo + 5glox + -9glox = 9glox + -9glox

Combine like terms: 5glox + -9glox = -4glox
-5glo + -4glox = 9glox + -9glox

Combine like terms: 9glox + -9glox = 0
-5glo + -4glox = 0

Factor out the Greatest Common Factor (GCF), '-1glo'.
-1glo(5 + 4x) = 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 '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Add '-4x' to each side of the equation. 4x + -4x = -5 + -4x Combine like terms: 4x + -4x = 0 0 = -5 + -4x Simplifying 0 = -5 + -4x 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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