What is log_{5}((sqrt(x))/(25y^3)) ?

The solution to log_{5}((sqrt(x))/(25y^3)) is log_{5}(sqrt(x))-2-3log_{5}(y)

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simplify log_{5}((sqrt(x))/(25y^3))

simplify

lo g_{5} (\frac{x}{25 y ^{3}})

lo g_{5} (x) - 2 - 3 lo g_{5} (y)

Solution steps

lo g_{5} (\frac{x}{25 y ^{3}})

Apply log rule:

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

lo g_{5} (\frac{x}{25 y ^{3}}) = lo g_{5} (x) - lo g_{5} (25 y^{3})

= lo g_{5} (x) - lo g_{5} (25 y^{3})

Simplify

lo g_{5} (25 y^{3}) : 2 + 3 lo g_{5} (y)

= lo g_{5} (x) - (2 + 3 lo g_{5} (y))

Apply the distributive law:

- (a + b) = - a - b

- (2 + 3 lo g_{5} (y)) = - 2 - 3 lo g_{5} (y)

= lo g_{5} (x) - 2 - 3 lo g_{5} (y)

ln (3) + ln (x)

2 ln (3) - 3 ln (2)

lo g_{10} (x) + lo g_{10} (y) + 3 lo g_{10} (z)

lo g_{b} (\frac{1}{10}) + lo g_{b} (40)

lo g_{2} (\frac{8}{x + 5})

What is log_{5}((sqrt(x))/(25y^3)) ?
The solution to log_{5}((sqrt(x))/(25y^3)) is log_{5}(sqrt(x))-2-3log_{5}(y)