Log(5)(2x-7)=Log(18)(x-9)

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Solution for Log(5)(2x-7)=Log(18)(x-9) equation: 


Simplifying
Log(5)(2x + -7) = Log(18)(x + -9)

Reorder the terms:
goL * 5(-7 + 2x) = Log(18)(x + -9)

Reorder the terms for easier multiplication:
5goL(-7 + 2x) = Log(18)(x + -9)
(-7 * 5goL + 2x * 5goL) = Log(18)(x + -9)
(-35goL + 10goxL) = Log(18)(x + -9)

Reorder the terms:
-35goL + 10goxL = goL * 18(-9 + x)

Reorder the terms for easier multiplication:
-35goL + 10goxL = 18goL(-9 + x)
-35goL + 10goxL = (-9 * 18goL + x * 18goL)
-35goL + 10goxL = (-162goL + 18goxL)

Solving
-35goL + 10goxL = -162goL + 18goxL

Solving for variable 'g'.

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

Add '162goL' to each side of the equation.
-35goL + 162goL + 10goxL = -162goL + 162goL + 18goxL

Combine like terms: -35goL + 162goL = 127goL
127goL + 10goxL = -162goL + 162goL + 18goxL

Combine like terms: -162goL + 162goL = 0
127goL + 10goxL = 0 + 18goxL
127goL + 10goxL = 18goxL

Add '-18goxL' to each side of the equation.
127goL + 10goxL + -18goxL = 18goxL + -18goxL

Combine like terms: 10goxL + -18goxL = -8goxL
127goL + -8goxL = 18goxL + -18goxL

Combine like terms: 18goxL + -18goxL = 0
127goL + -8goxL = 0

Factor out the Greatest Common Factor (GCF), 'goL'.
goL(127 + -8x) = 0


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

Simplifying
goL = 0

Solving
goL = 0

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

Simplifying
goL = 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 '(127 + -8x)' equal to zero and attempt to solve:

Simplifying
127 + -8x = 0

Solving
127 + -8x = 0

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

Add '-127' to each side of the equation.
127 + -127 + -8x = 0 + -127

Combine like terms: 127 + -127 = 0
0 + -8x = 0 + -127
-8x = 0 + -127

Combine like terms: 0 + -127 = -127
-8x = -127

Add '8x' to each side of the equation.
-8x + 8x = -127 + 8x

Combine like terms: -8x + 8x = 0
0 = -127 + 8x

Simplifying
0 = -127 + 8x

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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