log^5(7x-4)=log^5(5x-3)

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Solution for log^5(7x-4)=log^5(5x-3) equation: 


Simplifying
log5(7x + -4) = log5(5x + -3)

Reorder the terms:
g5lo(-4 + 7x) = log5(5x + -3)
(-4 * g5lo + 7x * g5lo) = log5(5x + -3)
(-4g5lo + 7g5lox) = log5(5x + -3)

Reorder the terms:
-4g5lo + 7g5lox = g5lo(-3 + 5x)
-4g5lo + 7g5lox = (-3 * g5lo + 5x * g5lo)
-4g5lo + 7g5lox = (-3g5lo + 5g5lox)

Solving
-4g5lo + 7g5lox = -3g5lo + 5g5lox

Solving for variable 'g'.

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

Add '3g5lo' to each side of the equation.
-4g5lo + 3g5lo + 7g5lox = -3g5lo + 3g5lo + 5g5lox

Combine like terms: -4g5lo + 3g5lo = -1g5lo
-1g5lo + 7g5lox = -3g5lo + 3g5lo + 5g5lox

Combine like terms: -3g5lo + 3g5lo = 0
-1g5lo + 7g5lox = 0 + 5g5lox
-1g5lo + 7g5lox = 5g5lox

Add '-5g5lox' to each side of the equation.
-1g5lo + 7g5lox + -5g5lox = 5g5lox + -5g5lox

Combine like terms: 7g5lox + -5g5lox = 2g5lox
-1g5lo + 2g5lox = 5g5lox + -5g5lox

Combine like terms: 5g5lox + -5g5lox = 0
-1g5lo + 2g5lox = 0

Factor out the Greatest Common Factor (GCF), 'g5lo'.
g5lo(-1 + 2x) = 0


Subproblem 1
Set the factor 'g5lo' equal to zero and attempt to solve:

Simplifying
g5lo = 0

Solving
g5lo = 0

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

Simplifying
g5lo = 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 '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x = 0 + 1
2x = 0 + 1

Combine like terms: 0 + 1 = 1
2x = 1

Add '-2x' to each side of the equation.
2x + -2x = 1 + -2x

Combine like terms: 2x + -2x = 0
0 = 1 + -2x

Simplifying
0 = 1 + -2x

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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