What is log_{10}((sqrt(x))/(100y^3)) ?

The solution to log_{10}((sqrt(x))/(100y^3)) is log_{10}(sqrt(x))-2-3log_{10}(y)

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simplify log_{10}((sqrt(x))/(100y^3))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= lo g_{10} (x) - lo g_{10} (100 y^{3})

Simplify

lo g_{10} (100 y^{3}) : 2 + 3 lo g_{10} (y)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

lo g_{5} (19 y)

lo g_{10} (\frac{( 23 \times 0.15 ) ^{2}}{234}) - 2

lo g_{10} (5 z^{5})

ln (\frac{x ( x ^{3} - 4 ) ^{5}}{( 1 - 2 x ) ^{3}})

\frac{lo g _{e} ( a ^{b} ) - lo g _{e} ( a ^{c} )}{b - c}

What is log_{10}((sqrt(x))/(100y^3)) ?
The solution to log_{10}((sqrt(x))/(100y^3)) is log_{10}(sqrt(x))-2-3log_{10}(y)