log(7x+9)=log(10x-20)

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Solution for log(7x+9)=log(10x-20) equation:


Simplifying
log(7x + 9) = log(10x + -20)

Reorder the terms:
glo(9 + 7x) = log(10x + -20)
(9 * glo + 7x * glo) = log(10x + -20)
(9glo + 7glox) = log(10x + -20)

Reorder the terms:
9glo + 7glox = glo(-20 + 10x)
9glo + 7glox = (-20 * glo + 10x * glo)
9glo + 7glox = (-20glo + 10glox)

Solving
9glo + 7glox = -20glo + 10glox

Solving for variable 'g'.

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

Add '20glo' to each side of the equation.
9glo + 20glo + 7glox = -20glo + 20glo + 10glox

Combine like terms: 9glo + 20glo = 29glo
29glo + 7glox = -20glo + 20glo + 10glox

Combine like terms: -20glo + 20glo = 0
29glo + 7glox = 0 + 10glox
29glo + 7glox = 10glox

Add '-10glox' to each side of the equation.
29glo + 7glox + -10glox = 10glox + -10glox

Combine like terms: 7glox + -10glox = -3glox
29glo + -3glox = 10glox + -10glox

Combine like terms: 10glox + -10glox = 0
29glo + -3glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(29 + -3x) = 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 '(29 + -3x)' equal to zero and attempt to solve: Simplifying 29 + -3x = 0 Solving 29 + -3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + -3x = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -3x = 0 + -29 -3x = 0 + -29 Combine like terms: 0 + -29 = -29 -3x = -29 Add '3x' to each side of the equation. -3x + 3x = -29 + 3x Combine like terms: -3x + 3x = 0 0 = -29 + 3x Simplifying 0 = -29 + 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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