What is log_{2}((4(x-1)^{1/2})/(x+4)) ?

The solution to log_{2}((4(x-1)^{1/2})/(x+4)) is 2+1/2 log_{2}(x-1)-log_{2}(x+4)

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simplify log_{2}((4(x-1)^{1/2})/(x+4))

simplify

lo g_{2} (\frac{4 ( x - 1 ) ^{\frac{1}{2}}}{x + 4})

2 + \frac{1}{2} lo g_{2} (x - 1) - lo g_{2} (x + 4)

Solution steps

lo g_{2} (\frac{4 ( x - 1 ) ^{\frac{1}{2}}}{x + 4})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{2} (\frac{4 ( x - 1 ) ^{\frac{1}{2}}}{x + 4}) = lo g_{2} (4 (x - 1)^{\frac{1}{2}}) - lo g_{2} (x + 4)

= lo g_{2} (4 (x - 1)^{\frac{1}{2}}) - lo g_{2} (x + 4)

Simplify

lo g_{2} (4 (x - 1)^{\frac{1}{2}}) : 2 + \frac{1}{2} lo g_{2} (x - 1)

= 2 + \frac{1}{2} lo g_{2} (x - 1) - lo g_{2} (x + 4)

- lo g_{10} (x + 6) + lo g_{10} (x - 5)

3 lo g_{10} (2 x)

2 lo g_{10} (x) - 3 + lo g_{10} (\frac{x}{10})

lo g_{8} (14 x)

What is log_{2}((4(x-1)^{1/2})/(x+4)) ?
The solution to log_{2}((4(x-1)^{1/2})/(x+4)) is 2+1/2 log_{2}(x-1)-log_{2}(x+4)