What is expand log_{5}((a^3)/(b^3)) ?

The solution to expand log_{5}((a^3)/(b^3)) is 3log_{5}(a)-3log_{5}(b)

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expand log_{5}((a^3)/(b^3))

expand

lo g_{5} (\frac{a ^{3}}{b ^{3}})

3 lo g_{5} (a) - 3 lo g_{5} (b)

Solution steps

lo g_{5} (\frac{a ^{3}}{b ^{3}})

Apply log rule:

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

lo g_{5} (\frac{a ^{3}}{b ^{3}}) = lo g_{5} (a^{3}) - lo g_{5} (b^{3})

= lo g_{5} (a^{3}) - lo g_{5} (b^{3})

Apply log rule:

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

lo g_{5} (a^{3}) = 3 lo g_{5} (a)

= 3 lo g_{5} (a) - lo g_{5} (b^{3})

Apply log rule:

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

lo g_{5} (b^{3}) = 3 lo g_{5} (b)

= 3 lo g_{5} (a) - 3 lo g_{5} (b)

\frac{1}{15} \cdot ln (\frac{2089174}{684005})

\frac{( ln ( - cos ( 2 ) ) - ln ( - cos ( 4 ) ) ) a cro}{2}

ln (\frac{47}{50})

\frac{π}{8} ln (3)

What is expand log_{5}((a^3)/(b^3)) ?
The solution to expand log_{5}((a^3)/(b^3)) is 3log_{5}(a)-3log_{5}(b)