What is log_{5}((4sqrt(x))/(36y^4)) ?

The solution to log_{5}((4sqrt(x))/(36y^4)) is log_{5}(sqrt(x))-2log_{5}(3)-4log_{5}(y)

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simplify log_{5}((4sqrt(x))/(36y^4))

simplify

lo g_{5} (\frac{4 x}{36 y ^{4}})

lo g_{5} (x) - 2 lo g_{5} (3) - 4 lo g_{5} (y)

Solution steps

lo g_{5} (\frac{4 x}{36 y ^{4}})

Factor the number:

36 = 4 \cdot 9

= lo g_{5} (\frac{4 x}{4 \cdot 9 y ^{4}})

Cancel the common factor:

4

= lo g_{5} (\frac{x}{9 y ^{4}})

Apply log rule:

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

lo g_{5} (\frac{x}{9 y ^{4}}) = lo g_{5} (x) - lo g_{5} (9 y^{4})

= lo g_{5} (x) - lo g_{5} (9 y^{4})

Simplify

lo g_{5} (9 y^{4}) : 2 lo g_{5} (3) + 4 lo g_{5} (y)

= lo g_{5} (x) - (2 lo g_{5} (3) + 4 lo g_{5} (y))

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{5} (3) + 4 lo g_{5} (y)) = - 2 lo g_{5} (3) - 4 lo g_{5} (y)

= lo g_{5} (x) - 2 lo g_{5} (3) - 4 lo g_{5} (y)

lo g_{10} (\frac{10000}{x ^{2} + y ^{2}})

lo g_{4} (z) - lo g_{4} (y)

- lo g_{10} (1.5 \cdot 1 0^{- 2})

ln (\frac{x ^{2} y ^{3}}{z ^{5}})

5 ln (10) + 4 - 5 ln (5) + 1

What is log_{5}((4sqrt(x))/(36y^4)) ?
The solution to log_{5}((4sqrt(x))/(36y^4)) is log_{5}(sqrt(x))-2log_{5}(3)-4log_{5}(y)