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

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

Popular >

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

simplify

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

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

Solution steps

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

Simplify

x^{5} : x^{2} x

= lo g_{10} (\frac{x ^{2} x}{( x + 6 ) ^{3}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{x ^{2} x}{( x + 6 ) ^{3}}) = lo g_{10} (x^{2} x) - lo g_{10} ((x + 6)^{3})

= lo g_{10} (x^{2} x) - lo g_{10} ((x + 6)^{3})

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

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

= 2 lo g_{10} (x) + lo g_{10} (x) - 3 lo g_{10} (x + 6)

lo g_{6} (\frac{m}{n})

ln ((1 + i)^{n})

lo g_{10} (5 x y)

\frac{1}{2} lo g_{c} (+ 5 lo g_{d} (x))

\frac{1}{4} [3 ln (x + 4) - ln (x) - ln (x^{2} - 25)]

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