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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{5} (x^{5}) = 5 lo g_{5} (x)

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

Apply log rule:

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

lo g_{5} (y^{4}) = 4 lo g_{5} (y)

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

ln (\frac{( 8.9 - 2 ) ^{2}}{∣ 8.9 - 3 ∣}) + C

2 ln (2) + \frac{9}{5} ln (4) + \frac{1}{5} ln (- 1)

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

lo g_{5} (x y^{2})

ln (\frac{2}{1 + y})

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