What is expand log_{7}((xy^5)^2) ?

The solution to expand log_{7}((xy^5)^2) is 2log_{7}(x)+10log_{7}(y)

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expand log_{7}((xy^5)^2)

expand

lo g_{7} ((x y^{5})^{2})

2 lo g_{7} (x) + 10 lo g_{7} (y)

Solution steps

lo g_{7} ((x y^{5})^{2})

Apply log rule:

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

lo g_{7} ((x y^{5})^{2}) = 2 lo g_{7} (x y^{5})

= 2 lo g_{7} (x y^{5})

Apply log rule:

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

2 lo g_{7} (x y^{5}) = 2 lo g_{7} (x) + 2 lo g_{7} (y^{5})

= 2 lo g_{7} (x) + 2 lo g_{7} (y^{5})

Apply log rule:

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

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

= 2 lo g_{7} (x) + 2 \cdot 5 lo g_{7} (y)

Multiply the numbers:

2 \cdot 5 = 10

= 2 lo g_{7} (x) + 10 lo g_{7} (y)

ln (\frac{800 - 1200}{300 - 1200})

0.77 + \frac{8.134 \cdot 298}{1 \cdot 96500} \cdot ln (\frac{1}{2})

(ln (2) + ln (3)) \frac{π}{8}

ln (\frac{x ^{7}}{x ^{2} - 16})

ln (36 \cdot 1 5^{\frac{1}{2}}) + c

What is expand log_{7}((xy^5)^2) ?
The solution to expand log_{7}((xy^5)^2) is 2log_{7}(x)+10log_{7}(y)