What is expand log_{8}((xy^2)^2) ?

The solution to expand log_{8}((xy^2)^2) is 2log_{8}(x)+4log_{8}(y)

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expand log_{8}((xy^2)^2)

expand

lo g_{8} ((x y^{2})^{2})

2 lo g_{8} (x) + 4 lo g_{8} (y)

Solution steps

lo g_{8} ((x y^{2})^{2})

Apply log rule:

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

lo g_{8} ((x y^{2})^{2}) = 2 lo g_{8} (x y^{2})

= 2 lo g_{8} (x y^{2})

Apply log rule:

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

2 lo g_{8} (x y^{2}) = 2 lo g_{8} (x) + 2 lo g_{8} (y^{2})

= 2 lo g_{8} (x) + 2 lo g_{8} (y^{2})

Apply log rule:

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

lo g_{8} (y^{2}) = 2 lo g_{8} (y)

= 2 lo g_{8} (x) + 2 \cdot 2 lo g_{8} (y)

Multiply the numbers:

2 \cdot 2 = 4

= 2 lo g_{8} (x) + 4 lo g_{8} (y)

ln (\frac{4000}{500})

- \frac{1}{3 ln ^{2} ( 3 )}

\frac{6}{5} ln \frac{y}{x} - 1 + ln ∣ x ∣

ln (5 \cdot 1 0^{- 7})

ln (1 \cdot \frac{46.7092}{48.20979})

What is expand log_{8}((xy^2)^2) ?
The solution to expand log_{8}((xy^2)^2) is 2log_{8}(x)+4log_{8}(y)