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Popular >

simplify log_{2}(10^{10})

Solution

simplify

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

Solution

10 + 10 lo g_{2} (5)

+1

Decimal Notation

33.21928 \dots

Solution steps

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

Apply log rule:

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

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

= 10 lo g_{2} (10)

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

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

Expand

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

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

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Frequently Asked Questions (FAQ)

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