What is log_{10}((sqrt(x))/(10000y^9)) ?

The solution to log_{10}((sqrt(x))/(10000y^9)) is log_{10}(sqrt(x))-4-9log_{10}(y)

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simplify log_{10}((sqrt(x))/(10000y^9))

simplify

lo g_{10} (\frac{x}{10000 y ^{9}})

lo g_{10} (x) - 4 - 9 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{10000 y ^{9}})

Apply log rule:

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

lo g_{10} (\frac{x}{10000 y ^{9}}) = lo g_{10} (x) - lo g_{10} (10000 y^{9})

= lo g_{10} (x) - lo g_{10} (10000 y^{9})

Simplify

lo g_{10} (10000 y^{9}) : 4 + 9 lo g_{10} (y)

= lo g_{10} (x) - (4 + 9 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (4 + 9 lo g_{10} (y)) = - 4 - 9 lo g_{10} (y)

= lo g_{10} (x) - 4 - 9 lo g_{10} (y)

lo g_{10} (\frac{x ^{6} y}{z})

lo g_{2} (3) + lo g_{2} (x)

ln (5 x) - ln (1)

ln (\frac{0.2}{0.1})

What is log_{10}((sqrt(x))/(10000y^9)) ?
The solution to log_{10}((sqrt(x))/(10000y^9)) is log_{10}(sqrt(x))-4-9log_{10}(y)