Log(4r+1)=log(5r-2)

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Solution for Log(4r+1)=log(5r-2) equation: 


Simplifying
Log(4r + 1) = log(5r + -2)

Reorder the terms:
goL(1 + 4r) = log(5r + -2)
(1 * goL + 4r * goL) = log(5r + -2)
(1goL + 4gorL) = log(5r + -2)

Reorder the terms:
1goL + 4gorL = glo(-2 + 5r)
1goL + 4gorL = (-2 * glo + 5r * glo)
1goL + 4gorL = (-2glo + 5glor)

Solving
1goL + 4gorL = -2glo + 5glor

Solving for variable 'g'.

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

Add '2glo' to each side of the equation.
1goL + 2glo + 4gorL = -2glo + 2glo + 5glor

Reorder the terms:
2glo + 1goL + 4gorL = -2glo + 2glo + 5glor

Combine like terms: -2glo + 2glo = 0
2glo + 1goL + 4gorL = 0 + 5glor
2glo + 1goL + 4gorL = 5glor

Add '-5glor' to each side of the equation.
2glo + 1goL + -5glor + 4gorL = 5glor + -5glor

Reorder the terms:
2glo + -5glor + 1goL + 4gorL = 5glor + -5glor

Combine like terms: 5glor + -5glor = 0
2glo + -5glor + 1goL + 4gorL = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(2l + -5lr + L + 4rL) = 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 '(2l + -5lr + L + 4rL)' equal to zero and attempt to solve:

Simplifying
2l + -5lr + L + 4rL = 0

Reorder the terms:
L + 2l + -5lr + 4rL = 0

Solving
L + 2l + -5lr + 4rL = 0

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

Add '-1L' to each side of the equation.
L + 2l + -5lr + -1L + 4rL = 0 + -1L

Reorder the terms:
L + -1L + 2l + -5lr + 4rL = 0 + -1L

Combine like terms: L + -1L = 0
0 + 2l + -5lr + 4rL = 0 + -1L
2l + -5lr + 4rL = 0 + -1L
Remove the zero:
2l + -5lr + 4rL = -1L

Add '-2l' to each side of the equation.
2l + -5lr + -2l + 4rL = -1L + -2l

Reorder the terms:
2l + -2l + -5lr + 4rL = -1L + -2l

Combine like terms: 2l + -2l = 0
0 + -5lr + 4rL = -1L + -2l
-5lr + 4rL = -1L + -2l

Add '5lr' to each side of the equation.
-5lr + 5lr + 4rL = -1L + -2l + 5lr

Combine like terms: -5lr + 5lr = 0
0 + 4rL = -1L + -2l + 5lr
4rL = -1L + -2l + 5lr

Add '-4rL' to each side of the equation.
4rL + -4rL = -1L + -2l + 5lr + -4rL

Combine like terms: 4rL + -4rL = 0
0 = -1L + -2l + 5lr + -4rL

Simplifying
0 = -1L + -2l + 5lr + -4rL

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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