SOLUTION: solve for x log2 (y+4) + log2 y =5

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Question 138396: solve for x
log2 (y+4) + log2 y =5
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
It is impossible, or at least way beyond my meager capabilities as a mathematician to solve an equation in y for x. I shall describe the process to solve it for y and hope that is sufficient.

log%282%2C%28y%2B4%29%29%2Blog%282%2C%28y%29%29=5

Rule: log%28b%2C%28a%29%29%2Blog%28b%2C%28c%29%29=log%28b%2C%28ac%29%29, so

log%282%2C%28y%5E2%2B4y%29%29=5

Rule: y=log%28b%2Cx%29 => b%5Ey=x, so

y%5E2%2B4y=2%5E5=32, or in standard form: y%5E2%2B4y-32=0

So, solve the quadratic to get your potential solutions. I say potential solutions because we squared the variable in the process of manipulating the equation. That means there is the possibility that we introduced an extraneous root. You need to take both roots and test them in the original equation remembering that the domain of f%28x%29=log%28b%2C%28x%29%29 is all POSITIVE reals.