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simplify 2log_{2}(3)-log_{2}(36)

Solution

simplify

2 lo g_{2} (3) - lo g_{2} (36)

Solution

- 2

Solution steps

2 lo g_{2} (3) - lo g_{2} (36)

Apply log rule:

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

2 lo g_{2} (3) = lo g_{2} (3^{2})

= lo g_{2} (3^{2}) - lo g_{2} (36)

Apply log rule:

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

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

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

\frac{3 ^{2}}{36} = 2^{- 2}

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

Apply log rule:

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

= - 2

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Frequently Asked Questions (FAQ)

What is 2log_{2}(3)-log_{2}(36) ?
The solution to 2log_{2}(3)-log_{2}(36) is -2