What is log_{10}((sqrt(x))/(1000y^7)) ?

The solution to log_{10}((sqrt(x))/(1000y^7)) is log_{10}(sqrt(x))-3-7log_{10}(y)

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simplify log_{10}((sqrt(x))/(1000y^7))

simplify

lo g_{10} (\frac{x}{1000 y ^{7}})

lo g_{10} (x) - 3 - 7 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{1000 y ^{7}})

Apply log rule:

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

lo g_{10} (\frac{x}{1000 y ^{7}}) = lo g_{10} (x) - lo g_{10} (1000 y^{7})

= lo g_{10} (x) - lo g_{10} (1000 y^{7})

Simplify

lo g_{10} (1000 y^{7}) : 3 + 7 lo g_{10} (y)

= lo g_{10} (x) - (3 + 7 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (3 + 7 lo g_{10} (y)) = - 3 - 7 lo g_{10} (y)

= lo g_{10} (x) - 3 - 7 lo g_{10} (y)

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What is log_{10}((sqrt(x))/(1000y^7)) ?
The solution to log_{10}((sqrt(x))/(1000y^7)) is log_{10}(sqrt(x))-3-7log_{10}(y)