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

The solution to expand log_{10}((sqrt(x^5))/((x+6)^3)) is log_{10}(sqrt(x)sqrt(x^4))-3log_{10}(x+6)

Popular >

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

expand

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

lo g_{10} (x x^{4}) - 3 lo g_{10} (x + 6)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

x^{5} = x x^{4}

= lo g_{10} (x x^{4}) - 3 lo g_{10} (x + 6)

ln (e^{x} cos (x))

- 2 ln (x) + ln (y)

3 lo g_{b} (x) - 4 lo g_{b} (y) + \frac{1}{2} lo g_{b} (x + y)

ln (\frac{10}{8})

ln (\frac{9}{13})

What is expand log_{10}((sqrt(x^5))/((x+6)^3)) ?
The solution to expand log_{10}((sqrt(x^5))/((x+6)^3)) is log_{10}(sqrt(x)sqrt(x^4))-3log_{10}(x+6)