Log[5](4x+1)=log[5](9x+5)

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Solution for Log[5](4x+1)=log[5](9x+5) equation:


Simplifying
Log[5](4x + 1) = log[5](9x + 5)

Reorder the terms:
goL * 5(1 + 4x) = log[5](9x + 5)

Reorder the terms for easier multiplication:
5goL(1 + 4x) = log[5](9x + 5)
(1 * 5goL + 4x * 5goL) = log[5](9x + 5)
(5goL + 20goxL) = log[5](9x + 5)

Reorder the terms:
5goL + 20goxL = glo * 5(5 + 9x)

Reorder the terms for easier multiplication:
5goL + 20goxL = 5glo(5 + 9x)
5goL + 20goxL = (5 * 5glo + 9x * 5glo)
5goL + 20goxL = (25glo + 45glox)

Solving
5goL + 20goxL = 25glo + 45glox

Solving for variable 'g'.

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

Add '-25glo' to each side of the equation.
5goL + -25glo + 20goxL = 25glo + -25glo + 45glox

Reorder the terms:
-25glo + 5goL + 20goxL = 25glo + -25glo + 45glox

Combine like terms: 25glo + -25glo = 0
-25glo + 5goL + 20goxL = 0 + 45glox
-25glo + 5goL + 20goxL = 45glox

Add '-45glox' to each side of the equation.
-25glo + 5goL + -45glox + 20goxL = 45glox + -45glox

Reorder the terms:
-25glo + -45glox + 5goL + 20goxL = 45glox + -45glox

Combine like terms: 45glox + -45glox = 0
-25glo + -45glox + 5goL + 20goxL = 0

Factor out the Greatest Common Factor (GCF), '5go'.
5go(-5l + -9lx + L + 4xL) = 0

Ignore the factor 5.

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 '(-5l + -9lx + L + 4xL)' equal to zero and attempt to solve: Simplifying -5l + -9lx + L + 4xL = 0 Reorder the terms: L + -5l + -9lx + 4xL = 0 Solving L + -5l + -9lx + 4xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-1L' to each side of the equation. L + -5l + -9lx + -1L + 4xL = 0 + -1L Reorder the terms: L + -1L + -5l + -9lx + 4xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -5l + -9lx + 4xL = 0 + -1L -5l + -9lx + 4xL = 0 + -1L Remove the zero: -5l + -9lx + 4xL = -1L Add '5l' to each side of the equation. -5l + -9lx + 5l + 4xL = -1L + 5l Reorder the terms: -5l + 5l + -9lx + 4xL = -1L + 5l Combine like terms: -5l + 5l = 0 0 + -9lx + 4xL = -1L + 5l -9lx + 4xL = -1L + 5l Add '9lx' to each side of the equation. -9lx + 9lx + 4xL = -1L + 5l + 9lx Combine like terms: -9lx + 9lx = 0 0 + 4xL = -1L + 5l + 9lx 4xL = -1L + 5l + 9lx Add '-4xL' to each side of the equation. 4xL + -4xL = -1L + 5l + 9lx + -4xL Combine like terms: 4xL + -4xL = 0 0 = -1L + 5l + 9lx + -4xL Simplifying 0 = -1L + 5l + 9lx + -4xL 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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