What is expand log_{7}((ab^6)^5) ?

The solution to expand log_{7}((ab^6)^5) is 5log_{7}(a)+30log_{7}(b)

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expand log_{7}((ab^6)^5)

expand

lo g_{7} ((a b^{6})^{5})

5 lo g_{7} (a) + 30 lo g_{7} (b)

Solution steps

lo g_{7} ((a b^{6})^{5})

Apply log rule:

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

lo g_{7} ((a b^{6})^{5}) = 5 lo g_{7} (a b^{6})

= 5 lo g_{7} (a b^{6})

Apply log rule:

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

5 lo g_{7} (a b^{6}) = 5 lo g_{7} (a) + 5 lo g_{7} (b^{6})

= 5 lo g_{7} (a) + 5 lo g_{7} (b^{6})

Apply log rule:

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

lo g_{7} (b^{6}) = 6 lo g_{7} (b)

= 5 lo g_{7} (a) + 5 \cdot 6 lo g_{7} (b)

Multiply the numbers:

5 \cdot 6 = 30

= 5 lo g_{7} (a) + 30 lo g_{7} (b)

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What is expand log_{7}((ab^6)^5) ?
The solution to expand log_{7}((ab^6)^5) is 5log_{7}(a)+30log_{7}(b)