What is log_{10}((sqrt(x))/(1000y^6)) ?

The solution to log_{10}((sqrt(x))/(1000y^6)) is log_{10}(sqrt(x))-3-6log_{10}(y)

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simplify log_{10}((sqrt(x))/(1000y^6))

simplify

lo g_{10} (\frac{x}{1000 y ^{6}})

lo g_{10} (x) - 3 - 6 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{1000 y ^{6}})

Apply log rule:

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

lo g_{10} (\frac{x}{1000 y ^{6}}) = lo g_{10} (x) - lo g_{10} (1000 y^{6})

= lo g_{10} (x) - lo g_{10} (1000 y^{6})

Simplify

lo g_{10} (1000 y^{6}) : 3 + 6 lo g_{10} (y)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

lo g_{2} (\frac{x ^{3} y ^{8}}{5})

\frac{ln ( x )}{2} - 4 ln (y) - \frac{1}{3} ln (x + 2)

- \frac{1}{2} + \frac{1}{4} lo g_{10} (0.1) + \frac{1}{2} lo g_{10} (a)

ln (9) + ln (x)

ln (2 e^{5})

What is log_{10}((sqrt(x))/(1000y^6)) ?
The solution to log_{10}((sqrt(x))/(1000y^6)) is log_{10}(sqrt(x))-3-6log_{10}(y)