What is expand log_{2}((sqrt(a-1))/9) ?

The solution to expand log_{2}((sqrt(a-1))/9) is log_{2}(sqrt(a-1))-2log_{2}(3)

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expand log_{2}((sqrt(a-1))/9)

expand

lo g_{2} (\frac{a - 1}{9})

lo g_{2} (a - 1) - 2 lo g_{2} (3)

Solution steps

lo g_{2} (\frac{a - 1}{9})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{2} (\frac{a - 1}{9}) = lo g_{2} (a - 1) - lo g_{2} (9)

= lo g_{2} (a - 1) - lo g_{2} (9)

lo g_{2} (9) = 2 lo g_{2} (3)

= lo g_{2} (a - 1) - 2 lo g_{2} (3)

lo g_{10} (2 π)

3.3 + lo g_{10} (\frac{0.3 - 0.05}{0.25 + 0.05})

- lo g_{10} (1.5 \cdot 1 0^{- 4})

- 0.4 lo g_{2} (0.4) - 0.6 lo g_{2} (0.6)

lo g_{5} (\frac{u}{v ^{5}})

What is expand log_{2}((sqrt(a-1))/9) ?
The solution to expand log_{2}((sqrt(a-1))/9) is log_{2}(sqrt(a-1))-2log_{2}(3)