For x?N, x>1 , and p=logxx+1 , q=logx+1x+2 then which one of the following is co

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Question
For x?N, x>1 , and p=logxx+1 , q=logx+1x+2 then which one of the following is correct?
Options
A. p < q
B. p = q
C. p > q
D. can't be determined

Correct Answer

p > q

Explanation

$\frac{k}{l} > \frac{k + 1}{l + 1}$ for (k,l) > 0 and k > l

Let k = x+1 and l = x

Therefore, $\frac{x + 1}{x} > \frac{(x + 1) + 1}{(x) + 1}$

(x + 1) > x

Therefore, $\frac{\log (x + 1)}{\log (x)} > \frac{\log (x + 2)}{\log (x + 1)}$

$? \log_{x} (x + 1) > \log_{x + 1} (x + 2)$

Logarithm problems

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3. A fast moving superfast express crosses another pasenger train in 20 seconds. The speed of faster train is 72 km/hr and speeds of slower train is 27 km/h. Also the length of faster ntrain is 100m, then find the length of the slower train if they are moving in the same direction.
Options
A. 100 m
B. 125 m
C. 150 m
D. 175 m

Discuss

4. If log 64 = 1.8061, then the value of log 16 will be (approx)?
Options
A. 1.9048
B. 1.2040
C. 0.9840
D. 1.4521

Discuss

6. What is the characteristic of the logarithm of 0.0000134?
Options
A. 5
B. -5
C. 6
D. -6

Discuss

7. Find value of log27 +log 8 +log1000log 120
Options
A. 1/2
B. 3/2
C. 2
D. 2/3

Discuss

Correct Answer: 3/2

Explanation:

$= \frac{\log \sqrt{3^{3}} + \log 2^{3} + \log \sqrt{10^{3}}}{\log (10 � 3 � 2^{2})}$

$= \frac{\log (3^{3})^{\frac{1}{2}} + \log 2^{3} + \log {(10^{3})}^{\frac{1}{2}}}{\log (10 � 3 � 2^{2})}$

$= \frac{\frac{1}{2} \log 3^{3} + 3 \log 2 + \frac{1}{2} \log 10^{3}}{\log 10 + \log 3 + \log 2^{2}}$

$= \frac{\frac{3}{2} (\log 3 + 2 \log 2 + \log 10)}{\log 3 + 2 \log 2 + \log 10}$ = $\frac{3}{2}$

8. The Value of logtan10+logtan20+??+logtan890 is
Options
A. -1
B. 0
C. 1/2
D. 1

Discuss

Correct Answer: 0

Explanation:

$= [\log \tan (1^{0}) + \log \tan (89^{0})] + [\log \tan (2^{0}) + \log \tan (88^{0})] + ? ? + [\log \tan (45^{0})]$

$= \log [\tan (1^{0}) � \tan (89^{0})] + \log [\tan (2^{0}) � \tan (88^{0})] + ? ? + \log (1)$

$[? \tan (90 - ?) = c o t ? a n d \tan (45^{0}) = 1]$

= log 1 + log 1 +.....+log 1

= 0.

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For x?N, x>1 , and p=logxx+1 , q=logx+1x+2 then which one of the following is correct?

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For x?N, x>1 , and p=logxx+1 , q=logx+1x+2 then which one of the following is correct?

Logarithm problems

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