What is expand log_{8}(((x^3y)/2)^2) ?

The solution to expand log_{8}(((x^3y)/2)^2) is 2(log_{8}(x^3y)-1/3)

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expand log_{8}(((x^3y)/2)^2)

expand

lo g_{8} ((\frac{x ^{3} y}{2})^{2})

2 (lo g_{8} (x^{3} y) - \frac{1}{3})

Solution steps

lo g_{8} ((\frac{x ^{3} y}{2})^{2})

Apply log rule:

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

lo g_{8} ((\frac{x ^{3} y}{2})^{2}) = 2 lo g_{8} (\frac{x ^{3} y}{2})

= 2 lo g_{8} (\frac{x ^{3} y}{2})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{8} (\frac{x ^{3} y}{2}) = lo g_{8} (x^{3} y) - lo g_{8} (2)

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

lo g_{8} (2) = \frac{1}{3}

= 2 (lo g_{8} (x^{3} y) - \frac{1}{3})

- lo g_{10} (4.15 \cdot 1 0^{- 3})

ln (f (6.01))

0.0259 \cdot ln (\frac{1 0 ^{15}}{1.5 \cdot 1 0 ^{10}})

lo g_{10} (x) + 2 lo g_{10} (y) + 3

ln (\frac{4}{48})

What is expand log_{8}(((x^3y)/2)^2) ?
The solution to expand log_{8}(((x^3y)/2)^2) is 2(log_{8}(x^3y)-1/3)