What is log_{5}(1/25 a^3b^2) ?

The solution to log_{5}(1/25 a^3b^2) is -2+3log_{5}(a)+2log_{5}(b)

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simplify log_{5}(1/25 a^3b^2)

simplify

lo g_{5} (\frac{1}{25} a^{3} b^{2})

- 2 + 3 lo g_{5} (a) + 2 lo g_{5} (b)

Solution steps

lo g_{5} (\frac{1}{25} a^{3} b^{2})

\frac{1}{25} = 5^{- 2}

= lo g_{5} (5^{- 2} a^{3} b^{2})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{5} (5^{- 2} a^{3} b^{2}) = lo g_{5} (5^{- 2}) + lo g_{5} (a^{3} b^{2})

= lo g_{5} (5^{- 2}) + lo g_{5} (a^{3} b^{2})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{5} (5^{- 2}) = - 2

= - 2 + lo g_{5} (a^{3} b^{2})

Simplify

lo g_{5} (a^{3} b^{2}) : 3 lo g_{5} (a) + 2 lo g_{5} (b)

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

Apply rule:

a + (b + c) = a + b + c

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

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

lo g_{9} ((\frac{u ^{4}}{w})^{4})

3 lo g_{10} (x) - lo g_{10} (\frac{1}{x})

lo g_{a} (ab)

\frac{1}{3} ln (12)

lo g_{2} (x (x - 1))

What is log_{5}(1/25 a^3b^2) ?
The solution to log_{5}(1/25 a^3b^2) is -2+3log_{5}(a)+2log_{5}(b)