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Popular >

simplify log_{2}(4n^2)

Solution

simplify

lo g_{2} (4 n^{2})

Solution

2 + 2 lo g_{2} (n)

Solution steps

lo g_{2} (4 n^{2})

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

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

= 2 + 2 lo g_{2} (n)

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29

Frequently Asked Questions (FAQ)

What is log_{2}(4n^2) ?
The solution to log_{2}(4n^2) is 2+2log_{2}(n)