What is expand log_{2}((xy)^{10}) ?

The solution to expand log_{2}((xy)^{10}) is 10log_{2}(x)+10log_{2}(y)

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expand log_{2}((xy)^{10})

expand

lo g_{2} ((x y)^{10})

10 lo g_{2} (x) + 10 lo g_{2} (y)

Solution steps

lo g_{2} ((x y)^{10})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{2} ((x y)^{10}) = 10 lo g_{2} (x y)

= 10 lo g_{2} (x y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

10 lo g_{2} (x y) = 10 lo g_{2} (x) + 10 lo g_{2} (y)

= 10 lo g_{2} (x) + 10 lo g_{2} (y)

9 ln (x) - 2 ln (y) + 5 ln (z^{3})

lo g_{4} (\frac{1}{16} x^{2} y^{3})

ln (\frac{5}{3}) + 4

lo g_{7} (9) + lo g_{7} (8)

f (x) = lo g_{10} (2 x) - lo g_{10} (8 x^{3})

What is expand log_{2}((xy)^{10}) ?
The solution to expand log_{2}((xy)^{10}) is 10log_{2}(x)+10log_{2}(y)