What is expand log_{7}((xy)^5) ?

The solution to expand log_{7}((xy)^5) is 5log_{7}(x)+5log_{7}(y)

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expand log_{7}((xy)^5)

expand

lo g_{7} ((x y)^{5})

5 lo g_{7} (x) + 5 lo g_{7} (y)

Solution steps

lo g_{7} ((x y)^{5})

Apply log rule:

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

lo g_{7} ((x y)^{5}) = 5 lo g_{7} (x y)

= 5 lo g_{7} (x y)

Apply log rule:

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

5 lo g_{7} (x y) = 5 lo g_{7} (x) + 5 lo g_{7} (y)

= 5 lo g_{7} (x) + 5 lo g_{7} (y)

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What is expand log_{7}((xy)^5) ?
The solution to expand log_{7}((xy)^5) is 5log_{7}(x)+5log_{7}(y)