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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- ln (57) + ln (123)

lo g_{e} (3 x + 1) + lo g_{e} (2)

\frac{1}{10} ln (10)

2 ln (53)

(100000 \cdot 0.25) \cdot ln (\frac{0.1}{0.25})

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