What is log_{10}((sqrt(10^2*1000))/(x^3*y^{-2)}) ?

The solution to log_{10}((sqrt(10^2*1000))/(x^3*y^{-2)}) is (4log_{10}(y)+5)/2-3log_{10}(x)

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simplify log_{10}((sqrt(10^21000))/(x^3y^{-2)})

simplify

lo g_{10} (\frac{1 0 ^{2} \cdot 1000}{x ^{3} \cdot y ^{- 2}})

\frac{4 lo g _{10} ( y ) + 5}{2} - 3 lo g_{10} (x)

Solution steps

lo g_{10} (\frac{1 0 ^{2} \cdot 1000}{x ^{3} y ^{- 2}})

Simplify

\frac{1 0 ^{2} \cdot 1000}{x ^{3} y ^{- 2}} : \frac{100 10 y ^{2}}{x ^{3}}

= lo g_{10} (\frac{100 10 y ^{2}}{x ^{3}})

Apply log rule:

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

lo g_{10} (\frac{100 10 y ^{2}}{x ^{3}}) = lo g_{10} (10010 y^{2}) - lo g_{10} (x^{3})

= lo g_{10} (10010 y^{2}) - lo g_{10} (x^{3})

lo g_{10} (10010 y^{2}) = \frac{4 lo g _{10} ( y ) + 5}{2}

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

= \frac{4 lo g _{10} ( y ) + 5}{2} - 3 lo g_{10} (x)

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

5 lo g_{2} (x) + \frac{3}{4} lo g_{2} (y) - lo g_{2} (z)

5 lo g_{10} (x) - 8 lo g_{10} (x + 1)

lo g_{4} (\frac{16}{x + 3})

What is log_{10}((sqrt(10^2*1000))/(x^3*y^{-2)}) ?
The solution to log_{10}((sqrt(10^2*1000))/(x^3*y^{-2)}) is (4log_{10}(y)+5)/2-3log_{10}(x)