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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{7}{4} \cdot ln (\frac{7}{4}) - \frac{1}{\frac{7}{4}}

- ln (4) + ln (\frac{1}{4})

ln (20) - ln (9)

lo g_{2} (x^{6} y^{4})

3 lo g_{5} (x + 2) - lo g_{5} (x)

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