What is log_{10}((sqrt(x))/(10y^5)) ?

The solution to log_{10}((sqrt(x))/(10y^5)) is log_{10}(sqrt(x))-1-5log_{10}(y)

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simplify log_{10}((sqrt(x))/(10y^5))

simplify

lo g_{10} (\frac{x}{10 y ^{5}})

lo g_{10} (x) - 1 - 5 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{10 y ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x}{10 y ^{5}}) = lo g_{10} (x) - lo g_{10} (10 y^{5})

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

Simplify

lo g_{10} (10 y^{5}) : 1 + 5 lo g_{10} (y)

= lo g_{10} (x) - (1 + 5 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (1 + 5 lo g_{10} (y)) = - 1 - 5 lo g_{10} (y)

= lo g_{10} (x) - 1 - 5 lo g_{10} (y)

lo g_{4} (x + 1) + lo g_{4} (4 x - 3)

lo g_{10} (10 x^{100}) 5

2 ln (x) - \frac{1}{7} ln (y)

lo g_{b} (\frac{1}{10}) + lo g_{b} (50)

lo g_{2} (5) + lo g_{2} (x)

What is log_{10}((sqrt(x))/(10y^5)) ?
The solution to log_{10}((sqrt(x))/(10y^5)) is log_{10}(sqrt(x))-1-5log_{10}(y)