What is expand log_{9}((4x)/(y^5)) ?

The solution to expand log_{9}((4x)/(y^5)) is 2log_{9}(2)+log_{9}(x)-5log_{9}(y)

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expand log_{9}((4x)/(y^5))

expand

lo g_{9} (\frac{4 x}{y ^{5}})

2 lo g_{9} (2) + lo g_{9} (x) - 5 lo g_{9} (y)

Solution steps

lo g_{9} (\frac{4 x}{y ^{5}})

Apply log rule:

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

lo g_{9} (\frac{4 x}{y ^{5}}) = lo g_{9} (4 x) - lo g_{9} (y^{5})

= lo g_{9} (4 x) - lo g_{9} (y^{5})

Apply log rule:

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

lo g_{9} (y^{5}) = 5 lo g_{9} (y)

= lo g_{9} (4 x) - 5 lo g_{9} (y)

Apply log rule:

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

lo g_{9} (4 x) = lo g_{9} (4) + lo g_{9} (x)

= lo g_{9} (4) + lo g_{9} (x) - 5 lo g_{9} (y)

lo g_{9} (4) = 2 lo g_{9} (2)

= 2 lo g_{9} (2) + lo g_{9} (x) - 5 lo g_{9} (y)

ln (2 (e^{e}))

3 lo g_{10} (a) + lo g_{10} (b) - \frac{1}{2} lo g_{10} (c)

\frac{1}{5} lo g_{8} (3)

lo g_{10} (x^{3}) - lo g_{10} (y^{4}) + lo g_{10} (z)

What is expand log_{9}((4x)/(y^5)) ?
The solution to expand log_{9}((4x)/(y^5)) is 2log_{9}(2)+log_{9}(x)-5log_{9}(y)