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Popular >

simplify log_{2}(10^9)

Solution

simplify

lo g_{2} (1 0^{9})

Solution

9 + 9 lo g_{2} (5)

+1

Decimal Notation

29.89735 \dots

Solution steps

lo g_{2} (1 0^{9})

Apply log rule:

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

lo g_{2} (1 0^{9}) = 9 lo g_{2} (10)

= 9 lo g_{2} (10)

lo g_{2} (10) = 1 + lo g_{2} (5)

= 9 (1 + lo g_{2} (5))

Expand

9 (1 + lo g_{2} (5)) : 9 + 9 lo g_{2} (5)

= 9 + 9 lo g_{2} (5)

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Frequently Asked Questions (FAQ)

What is log_{2}(10^9) ?
The solution to log_{2}(10^9) is 9+9log_{2}(5)