log(3)(5x-3)=log(3)(8x+9)

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Solution for log(3)(5x-3)=log(3)(8x+9) equation:


Simplifying
log(3)(5x + -3) = log(3)(8x + 9)

Reorder the terms:
glo * 3(-3 + 5x) = log(3)(8x + 9)

Reorder the terms for easier multiplication:
3glo(-3 + 5x) = log(3)(8x + 9)
(-3 * 3glo + 5x * 3glo) = log(3)(8x + 9)
(-9glo + 15glox) = log(3)(8x + 9)

Reorder the terms:
-9glo + 15glox = glo * 3(9 + 8x)

Reorder the terms for easier multiplication:
-9glo + 15glox = 3glo(9 + 8x)
-9glo + 15glox = (9 * 3glo + 8x * 3glo)
-9glo + 15glox = (27glo + 24glox)

Solving
-9glo + 15glox = 27glo + 24glox

Solving for variable 'g'.

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

Add '-27glo' to each side of the equation.
-9glo + -27glo + 15glox = 27glo + -27glo + 24glox

Combine like terms: -9glo + -27glo = -36glo
-36glo + 15glox = 27glo + -27glo + 24glox

Combine like terms: 27glo + -27glo = 0
-36glo + 15glox = 0 + 24glox
-36glo + 15glox = 24glox

Add '-24glox' to each side of the equation.
-36glo + 15glox + -24glox = 24glox + -24glox

Combine like terms: 15glox + -24glox = -9glox
-36glo + -9glox = 24glox + -24glox

Combine like terms: 24glox + -24glox = 0
-36glo + -9glox = 0

Factor out the Greatest Common Factor (GCF), '-9glo'.
-9glo(4 + x) = 0

Ignore the factor -9.

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