What is expand log_{9}(((u^4)/w)^4) ?

The solution to expand log_{9}(((u^4)/w)^4) is 4(4log_{9}(u)-log_{9}(w))

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expand log_{9}(((u^4)/w)^4)

expand

lo g_{9} ((\frac{u ^{4}}{w})^{4})

4 (4 lo g_{9} (u) - lo g_{9} (w))

Solution steps

lo g_{9} ((\frac{u ^{4}}{w})^{4})

Apply log rule:

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

lo g_{9} ((\frac{u ^{4}}{w})^{4}) = 4 lo g_{9} (\frac{u ^{4}}{w})

= 4 lo g_{9} (\frac{u ^{4}}{w})

Apply log rule:

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

lo g_{9} (\frac{u ^{4}}{w}) = lo g_{9} (u^{4}) - lo g_{9} (w)

= 4 (lo g_{9} (u^{4}) - lo g_{9} (w))

Apply log rule:

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

lo g_{9} (u^{4}) = 4 lo g_{9} (u)

= 4 (4 lo g_{9} (u) - lo g_{9} (w))

3 lo g_{10} (x) - lo g_{10} (\frac{1}{x})

lo g_{a} (ab)

\frac{1}{3} ln (12)

lo g_{2} (x (x - 1))

ln (x^{2} x^{2} - 2)

What is expand log_{9}(((u^4)/w)^4) ?
The solution to expand log_{9}(((u^4)/w)^4) is 4(4log_{9}(u)-log_{9}(w))