Log & Combination

Probability Level 3

Evaluate log ⁡ 4 ( ∑ k = 17 33 ( 33 k ) ) . \log_4 \left(\sum_{k=17}^{33} {33 \choose k}\right).

15 18 17 16

Ajay Dutta by Ajay Dutta , 24, India

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2 solutions

Matthew Henry
Jan 10, 2017

The sum is equal to the second half of row 33 of Pascal's triangle. The sum of which is 2^33.

Next I changed the base of the exponent to 4 to get cancel out the logarithm: 2^33 = 2^2^16 = 4^16

So the logarithm is then equal to 16

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2^33 is not equal to 4^16

Jessica Thomas - 4 years, 4 months ago
Lakshay Kharayat
Nov 9, 2016

Tukka bheda tha 😎😎😎

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