What is expand log_{5}((x^6)/(y^5)) ?

The solution to expand log_{5}((x^6)/(y^5)) is 6log_{5}(x)-5log_{5}(y)

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expand log_{5}((x^6)/(y^5))

expand

lo g_{5} (\frac{x ^{6}}{y ^{5}})

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

Solution steps

lo g_{5} (\frac{x ^{6}}{y ^{5}})

Apply log rule:

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

lo g_{5} (\frac{x ^{6}}{y ^{5}}) = lo g_{5} (x^{6}) - lo g_{5} (y^{5})

= lo g_{5} (x^{6}) - lo g_{5} (y^{5})

Apply log rule:

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

lo g_{5} (x^{6}) = 6 lo g_{5} (x)

= 6 lo g_{5} (x) - lo g_{5} (y^{5})

Apply log rule:

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

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

= 6 lo g_{5} (x) - 5 lo g_{5} (y)

3.5 + lo g_{10} (\frac{0.09949}{0.001})

2 (lo g_{6} (x) - 4 lo g_{6} (y)) + 3 lo g_{6} (z)

- lo g_{10} (3.4 \cdot 1 0^{- 9})

ln (\frac{100 + 0.55}{0.55})

What is expand log_{5}((x^6)/(y^5)) ?
The solution to expand log_{5}((x^6)/(y^5)) is 6log_{5}(x)-5log_{5}(y)