Log[3](5x-7)-Log[3](x+2)=1

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Solution for Log[3](5x-7)-Log[3](x+2)=1 equation:


Simplifying
Log[3](5x + -7) + -1Log[3](x + 2) = 1

Reorder the terms:
goL * 3(-7 + 5x) + -1Log[3](x + 2) = 1

Reorder the terms for easier multiplication:
3goL(-7 + 5x) + -1Log[3](x + 2) = 1
(-7 * 3goL + 5x * 3goL) + -1Log[3](x + 2) = 1
(-21goL + 15goxL) + -1Log[3](x + 2) = 1

Reorder the terms:
-21goL + 15goxL + -1goL * 3(2 + x) = 1

Reorder the terms for easier multiplication:
-21goL + 15goxL + -1 * 3goL(2 + x) = 1

Multiply -1 * 3
-21goL + 15goxL + -3goL(2 + x) = 1
-21goL + 15goxL + (2 * -3goL + x * -3goL) = 1
-21goL + 15goxL + (-6goL + -3goxL) = 1

Reorder the terms:
-21goL + -6goL + 15goxL + -3goxL = 1

Combine like terms: -21goL + -6goL = -27goL
-27goL + 15goxL + -3goxL = 1

Combine like terms: 15goxL + -3goxL = 12goxL
-27goL + 12goxL = 1

Solving
-27goL + 12goxL = 1

Solving for variable 'g'.

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

Reorder the terms:
-1 + -27goL + 12goxL = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -27goL + 12goxL = 0

The solution to this equation could not be determined.

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