What is log_{2}(12x^5y^{-2}) ?

The solution to log_{2}(12x^5y^{-2}) is 2+log_{2}(3)+5log_{2}(x)-2log_{2}(y)

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simplify log_{2}(12x^5y^{-2})

simplify

lo g_{2} (12 x^{5} y^{- 2})

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

Solution steps

lo g_{2} (12 x^{5} y^{- 2})

Factor the number:

12 = 2^{2} \cdot 3

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

Apply rule:

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

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

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

lo g_{10} (B^{- 5})

x^{3} y^{3} z^{3} + ln (y^{5} z^{4})

lo g_{7} (49 x yz)

2 lo g_{a} (9 x^{2}) - \frac{1}{6} lo g_{a} (7 x + 3)

lo g_{b} (m) - lo g_{b} (n)

What is log_{2}(12x^5y^{-2}) ?
The solution to log_{2}(12x^5y^{-2}) is 2+log_{2}(3)+5log_{2}(x)-2log_{2}(y)