If p+q=15, then what is q-p equal to?
For the following two (02) items: Let p = \sum_{j=1}^{n} \log_{10} 2^j and q = \sum_{j=1}^{n} \log_{10} 5^j.
- A. \log_{10} 2.5
- B. 5 \log_{10} 2.5
- C. 10 \log_{10} 2.5
- D. 15 \log_{10} 2.5 ✓
Correct Answer: D. 15 \log_{10} 2.5
Explanation
From \frac{n(n+1)}{2} = 15, we get n(n+1) = 30, so n=5. Now q-p = \sum_{j=1}^n (\log_{10} 5^j - \log_{10} 2^j) = \sum_{j=1}^n \log_{10}(2.5^j) = \log_{10}(2.5) \sum_{j=1}^n j. Thus q-p = 15 \log_{10} 2.5.
Related questions on Algebra
- How many four-digit natural numbers are there such that <strong>ALL</strong> of the digits are odd?
- What is \sum_{r=0}^{n}2^{r}C(n,r) equal to ?
- If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) a...
- Consider the following statements : 1. If f is the subset of Z\times Z defined by f=\{(xy,x-y);x,y\in Z\}, then f is a function from...
- For how many quadratic equations, the sum of roots is equal to the product of roots?