What is log_{10}((sqrt(x))/(100000y^8)) ?

The solution to log_{10}((sqrt(x))/(100000y^8)) is log_{10}(sqrt(x))-5-8log_{10}(y)

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simplify log_{10}((sqrt(x))/(100000y^8))

simplify

lo g_{10} (\frac{x}{100000 y ^{8}})

lo g_{10} (x) - 5 - 8 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{100000 y ^{8}})

Apply log rule:

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

lo g_{10} (\frac{x}{100000 y ^{8}}) = lo g_{10} (x) - lo g_{10} (100000 y^{8})

= lo g_{10} (x) - lo g_{10} (100000 y^{8})

Simplify

lo g_{10} (100000 y^{8}) : 5 + 8 lo g_{10} (y)

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

Apply the distributive law:

- (a + b) = - a - b

- (5 + 8 lo g_{10} (y)) = - 5 - 8 lo g_{10} (y)

= lo g_{10} (x) - 5 - 8 lo g_{10} (y)

ln (1000) + ln (\frac{1}{e}) + lo g_{3} (27)

ln (\frac{1}{1 + 3})

lo g_{10} (8 x^{2} yz)

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

- ln (\frac{e ^{2} - 1}{2 e ^{2}})

What is log_{10}((sqrt(x))/(100000y^8)) ?
The solution to log_{10}((sqrt(x))/(100000y^8)) is log_{10}(sqrt(x))-5-8log_{10}(y)