What is expand log_{8}(((u^6)/v)^4) ?

The solution to expand log_{8}(((u^6)/v)^4) is 4(6log_{8}(u)-log_{8}(v))

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expand log_{8}(((u^6)/v)^4)

expand

lo g_{8} ((\frac{u ^{6}}{v})^{4})

4 (6 lo g_{8} (u) - lo g_{8} (v))

Solution steps

lo g_{8} ((\frac{u ^{6}}{v})^{4})

Apply log rule:

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

lo g_{8} ((\frac{u ^{6}}{v})^{4}) = 4 lo g_{8} (\frac{u ^{6}}{v})

= 4 lo g_{8} (\frac{u ^{6}}{v})

Apply log rule:

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

lo g_{8} (\frac{u ^{6}}{v}) = lo g_{8} (u^{6}) - lo g_{8} (v)

= 4 (lo g_{8} (u^{6}) - lo g_{8} (v))

Apply log rule:

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

lo g_{8} (u^{6}) = 6 lo g_{8} (u)

= 4 (6 lo g_{8} (u) - lo g_{8} (v))

ln (\frac{3 x - 5}{2 x + 1})

ln ((x^{4} + 5) (x^{2} - 1)^{2})

5 ln (x) + 6 ln (y) + 9 ln (z)

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

ln (4.64) - ln (10.733)

What is expand log_{8}(((u^6)/v)^4) ?
The solution to expand log_{8}(((u^6)/v)^4) is 4(6log_{8}(u)-log_{8}(v))