What is expand log_{10}((sqrt(x^3))/((x+6)^5)) ?

The solution to expand log_{10}((sqrt(x^3))/((x+6)^5)) is log_{10}(sqrt(x)sqrt(x^2))-5log_{10}(x+6)

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expand log_{10}((sqrt(x^3))/((x+6)^5))

expand

lo g_{10} (\frac{x ^{3}}{( x + 6 ) ^{5}})

lo g_{10} (x x^{2}) - 5 lo g_{10} (x + 6)

Solution steps

lo g_{10} (\frac{x ^{3}}{( x + 6 ) ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x ^{3}}{( x + 6 ) ^{5}}) = lo g_{10} (x^{3}) - lo g_{10} ((x + 6)^{5})

= lo g_{10} (x^{3}) - lo g_{10} ((x + 6)^{5})

Apply log rule:

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

lo g_{10} ((x + 6)^{5}) = 5 lo g_{10} (x + 6)

= lo g_{10} (x^{3}) - 5 lo g_{10} (x + 6)

x^{3} = x x^{2}

= lo g_{10} (x x^{2}) - 5 lo g_{10} (x + 6)

ln (\frac{1 + sin ( x )}{cos ( x )})

lo g_{10} (\frac{9 a ^{16}}{b ^{2}})

lo g_{10} (\frac{x}{1})

ln^{2} (2 x)

What is expand log_{10}((sqrt(x^3))/((x+6)^5)) ?
The solution to expand log_{10}((sqrt(x^3))/((x+6)^5)) is log_{10}(sqrt(x)sqrt(x^2))-5log_{10}(x+6)