What is log_{2}(5)+1/2 log_{2}(36)-log_{2}(10) ?

The solution to log_{2}(5)+1/2 log_{2}(36)-log_{2}(10) is log_{2}(3)

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simplify log_{2}(5)+1/2 log_{2}(36)-log_{2}(10)

simplify

lo g_{2} (5) + \frac{1}{2} lo g_{2} (36) - lo g_{2} (10)

lo g_{2} (3)

Decimal Notation

1.58496 \dots

Solution steps

lo g_{2} (5) + \frac{1}{2} lo g_{2} (36) - lo g_{2} (10)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

\frac{1}{2} lo g_{2} (36) = lo g_{2} (3 6^{\frac{1}{2}})

= lo g_{2} (5) + lo g_{2} (3 6^{\frac{1}{2}}) - lo g_{2} (10)

Apply log rule:

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

lo g_{2} (5) + lo g_{2} (3 6^{\frac{1}{2}}) = lo g_{2} (5 \cdot 3 6^{\frac{1}{2}})

= lo g_{2} (5 \cdot 3 6^{\frac{1}{2}}) - lo g_{2} (10)

Apply log rule:

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

lo g_{2} (5 \cdot 3 6^{\frac{1}{2}}) - lo g_{2} (10) = lo g_{2} (\frac{5 \cdot 3 6 ^{\frac{1}{2}}}{10})

= lo g_{2} (\frac{5 \cdot 3 6 ^{\frac{1}{2}}}{10})

Cancel

\frac{5 \cdot 3 6 ^{\frac{1}{2}}}{10} : 3

= lo g_{2} (3)

lo g_{4} (16 y z^{3})

lo g_{10} (5 x + 8) - lo g_{10} (x)

lo g_{4} (\frac{z}{16})

lo g_{8} (64 x^{5})

- lo g_{10} (1.7 \cdot 1 0^{- 5})

What is log_{2}(5)+1/2 log_{2}(36)-log_{2}(10) ?
The solution to log_{2}(5)+1/2 log_{2}(36)-log_{2}(10) is log_{2}(3)