Log^5(3x+7)=log^5(4x+5)

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


Simplifying
Log5(3x + 7) = log5(4x + 5)

Reorder the terms:
g5oL(7 + 3x) = log5(4x + 5)
(7 * g5oL + 3x * g5oL) = log5(4x + 5)
(7g5oL + 3g5oxL) = log5(4x + 5)

Reorder the terms:
7g5oL + 3g5oxL = g5lo(5 + 4x)
7g5oL + 3g5oxL = (5 * g5lo + 4x * g5lo)
7g5oL + 3g5oxL = (5g5lo + 4g5lox)

Solving
7g5oL + 3g5oxL = 5g5lo + 4g5lox

Solving for variable 'g'.

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

Add '-5g5lo' to each side of the equation.
7g5oL + -5g5lo + 3g5oxL = 5g5lo + -5g5lo + 4g5lox

Reorder the terms:
-5g5lo + 7g5oL + 3g5oxL = 5g5lo + -5g5lo + 4g5lox

Combine like terms: 5g5lo + -5g5lo = 0
-5g5lo + 7g5oL + 3g5oxL = 0 + 4g5lox
-5g5lo + 7g5oL + 3g5oxL = 4g5lox

Add '-4g5lox' to each side of the equation.
-5g5lo + 7g5oL + -4g5lox + 3g5oxL = 4g5lox + -4g5lox

Reorder the terms:
-5g5lo + -4g5lox + 7g5oL + 3g5oxL = 4g5lox + -4g5lox

Combine like terms: 4g5lox + -4g5lox = 0
-5g5lo + -4g5lox + 7g5oL + 3g5oxL = 0

Factor out the Greatest Common Factor (GCF), 'g5o'.
g5o(-5l + -4lx + 7L + 3xL) = 0


Subproblem 1
Set the factor 'g5o' equal to zero and attempt to solve:

Simplifying
g5o = 0

Solving
g5o = 0

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

Simplifying
g5o = 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 + -4lx + 7L + 3xL)' equal to zero and attempt to solve:

Simplifying
-5l + -4lx + 7L + 3xL = 0

Reorder the terms:
7L + -5l + -4lx + 3xL = 0

Solving
7L + -5l + -4lx + 3xL = 0

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

Add '-7L' to each side of the equation.
7L + -5l + -4lx + -7L + 3xL = 0 + -7L

Reorder the terms:
7L + -7L + -5l + -4lx + 3xL = 0 + -7L

Combine like terms: 7L + -7L = 0
0 + -5l + -4lx + 3xL = 0 + -7L
-5l + -4lx + 3xL = 0 + -7L
Remove the zero:
-5l + -4lx + 3xL = -7L

Add '5l' to each side of the equation.
-5l + -4lx + 5l + 3xL = -7L + 5l

Reorder the terms:
-5l + 5l + -4lx + 3xL = -7L + 5l

Combine like terms: -5l + 5l = 0
0 + -4lx + 3xL = -7L + 5l
-4lx + 3xL = -7L + 5l

Add '4lx' to each side of the equation.
-4lx + 4lx + 3xL = -7L + 5l + 4lx

Combine like terms: -4lx + 4lx = 0
0 + 3xL = -7L + 5l + 4lx
3xL = -7L + 5l + 4lx

Add '-3xL' to each side of the equation.
3xL + -3xL = -7L + 5l + 4lx + -3xL

Combine like terms: 3xL + -3xL = 0
0 = -7L + 5l + 4lx + -3xL

Simplifying
0 = -7L + 5l + 4lx + -3xL

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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