What is expand log_{2}((sqrt(a^2-4))/9) ?

The solution to expand log_{2}((sqrt(a^2-4))/9) is log_{2}(sqrt(a^2-4))-2log_{2}(3)

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expand log_{2}((sqrt(a^2-4))/9)

expand

lo g_{2} (\frac{a ^{2} - 4}{9})

lo g_{2} (a^{2} - 4) - 2 lo g_{2} (3)

Solution steps

lo g_{2} (\frac{a ^{2} - 4}{9})

Apply log rule:

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

lo g_{2} (\frac{a ^{2} - 4}{9}) = lo g_{2} (a^{2} - 4) - lo g_{2} (9)

= lo g_{2} (a^{2} - 4) - lo g_{2} (9)

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

= lo g_{2} (a^{2} - 4) - 2 lo g_{2} (3)

\frac{1}{3} lo g_{c} (x) + 2 lo g_{c} (y) - 4 lo g_{c} (x)

lo g_{10} (3) + lo g_{10} (6) - lo g_{10} (2)

ln (y^{3}) + \frac{1}{3} ln (x^{3} y^{6}) - 5 ln (y)

lo g_{10} (x) - 3 lo g_{10} (2 y) + 4 lo g_{10} (z)

3 ln (2) + 4 ln (x) - ln (5) - 2 ln (y)

What is expand log_{2}((sqrt(a^2-4))/9) ?
The solution to expand log_{2}((sqrt(a^2-4))/9) is log_{2}(sqrt(a^2-4))-2log_{2}(3)