What is expand log_{8}((9x^2)/(y^3)) ?

The solution to expand log_{8}((9x^2)/(y^3)) is 2log_{8}(3)+2log_{8}(x)-3log_{8}(y)

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expand log_{8}((9x^2)/(y^3))

expand

lo g_{8} (\frac{9 x ^{2}}{y ^{3}})

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

Solution steps

lo g_{8} (\frac{9 x ^{2}}{y ^{3}})

Apply log rule:

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

lo g_{8} (\frac{9 x ^{2}}{y ^{3}}) = lo g_{8} (9 x^{2}) - lo g_{8} (y^{3})

= lo g_{8} (9 x^{2}) - lo g_{8} (y^{3})

Apply log rule:

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

lo g_{8} (y^{3}) = 3 lo g_{8} (y)

= lo g_{8} (9 x^{2}) - 3 lo g_{8} (y)

Apply log rule:

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

lo g_{8} (9 x^{2}) = lo g_{8} (9) + lo g_{8} (x^{2})

= lo g_{8} (9) + lo g_{8} (x^{2}) - 3 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)

= lo g_{8} (9) + 2 lo g_{8} (x) - 3 lo g_{8} (y)

lo g_{8} (9) = 2 lo g_{8} (3)

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

\frac{1}{3} ln (n^{2} + 8) - \frac{1}{3} ln (7 n^{2} + 5)

lo g_{2} (\frac{s ^{5}}{7 t ^{2}})

ln (\frac{e x + 1}{e x - 1})

lo g_{2} (1.5 \cdot a)

10 ln (\frac{2 \cdot 1 0 ^{- 7}}{1 0 ^{- 12}})

What is expand log_{8}((9x^2)/(y^3)) ?
The solution to expand log_{8}((9x^2)/(y^3)) is 2log_{8}(3)+2log_{8}(x)-3log_{8}(y)