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Expert: Robi Bhattacharjee - 9/12/2008


Question
"Describe how to obtain the third answer in each row from the first two answers"
a)log[base7]49, log[base49]49, log[base343]49
b) log[base4]64, log[base8]64, log[base32]64
How do i find the base for the third terms? Thanks

Answer
Hello Emily,

For a) you notice that 7 is 7^1 and 49 is 7^2. This means that the third term should have base 7^3 which is 343.


For b) it doesn't make sense. I would need to see another few terms before the pattern becomes clear. you see, 4 = 2^2 8 = 2^3 but 32 = 2^5. So it skips four for no apparent reason, so you need more information.


I hope this helped,

Robi

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Robi Bhattacharjee

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I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

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I am in the San Diego Math Circle

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I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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