What is log_{2}(6a^2y^4) ?

The solution to log_{2}(6a^2y^4) is 1+log_{2}(3)+2log_{2}(a)+4log_{2}(y)

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simplify log_{2}(6a^2y^4)

simplify

lo g_{2} (6 a^{2} y^{4})

1 + lo g_{2} (3) + 2 lo g_{2} (a) + 4 lo g_{2} (y)

Solution steps

lo g_{2} (6 a^{2} y^{4})

Factor the number:

6 = 2 \cdot 3

= lo g_{2} (2 \cdot 3 a^{2} y^{4})

Apply log rule:

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

lo g_{2} (2 \cdot 3 a^{2} y^{4}) = lo g_{2} (2) + lo g_{2} (3 a^{2} y^{4})

= lo g_{2} (2) + lo g_{2} (3 a^{2} y^{4})

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= 1 + lo g_{2} (3 a^{2} y^{4})

Simplify

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

= 1 + (lo g_{2} (3) + 2 lo g_{2} (a) + 4 lo g_{2} (y))

Apply rule:

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

1 + (lo g_{2} (3) + 2 lo g_{2} (a) + 4 lo g_{2} (y)) = 1 + lo g_{2} (3) + 2 lo g_{2} (a) + 4 lo g_{2} (y)

= 1 + lo g_{2} (3) + 2 lo g_{2} (a) + 4 lo g_{2} (y)

lo g_{3} (c) + lo g_{3} (c + 9)

ln (s t) + ln (\frac{s}{e})

lo g_{4} (x y)

lo g_{6} (\frac{216}{y})

ln (x) + ln (y) + ln (w) + 6 ln (z)

What is log_{2}(6a^2y^4) ?
The solution to log_{2}(6a^2y^4) is 1+log_{2}(3)+2log_{2}(a)+4log_{2}(y)