What is expand log_{5}((a^5)/(b^8)) ?

The solution to expand log_{5}((a^5)/(b^8)) is 5log_{5}(a)-8log_{5}(b)

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expand log_{5}((a^5)/(b^8))

expand

lo g_{5} (\frac{a ^{5}}{b ^{8}})

5 lo g_{5} (a) - 8 lo g_{5} (b)

Solution steps

lo g_{5} (\frac{a ^{5}}{b ^{8}})

Apply log rule:

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

lo g_{5} (\frac{a ^{5}}{b ^{8}}) = lo g_{5} (a^{5}) - lo g_{5} (b^{8})

= lo g_{5} (a^{5}) - lo g_{5} (b^{8})

Apply log rule:

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

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

= 5 lo g_{5} (a) - lo g_{5} (b^{8})

Apply log rule:

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

lo g_{5} (b^{8}) = 8 lo g_{5} (b)

= 5 lo g_{5} (a) - 8 lo g_{5} (b)

lo g_{5} (\frac{x ^{2} ( 1 - 5 x ) ^{\frac{3}{2}}}{x ^{2} - x})

ln (\frac{21}{10})

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

0.8 + 1.2 \cdot ln (\frac{4 8 ^{2}}{3 3 ^{2}})

ln \frac{y}{x} + 4 - 6 ln \frac{y}{x} - 1

What is expand log_{5}((a^5)/(b^8)) ?
The solution to expand log_{5}((a^5)/(b^8)) is 5log_{5}(a)-8log_{5}(b)