Register

CAT 2003 | Question: 2-96

• edited by
1,803 views
1 1 vote

What is the sum of '$n$' terms in the series: $\log m + \log \frac{m^2}{n} + \log \frac{m^3}{n^2} + \log \frac{m^4}{n^3} + \dots + \log \frac{m^n}{n^{n-1}}?$

  1. $\log \left[\frac{n^{n-1}}{m^{(n+1)}} \right]^{\frac{n}{2}}$
  2. $\log \left[\frac{m^m}{n^n} \right]^{\frac{n}{2}}$
  3. $\log \left[\frac{m^{(1-n)}}{n^{(1-m)}} \right]^{\frac{n}{2}}$
  4. $\log \left[\frac{m^{(n+1)}}{n^{(n-1)}} \right]^{\frac{n}{2}}$

1 Answer

0 0 votes

 

log m + log (m^2/n) + log (m^3/n^2)+log(m^4/n^3 )+......log(m^n/n^n-1)
  
=> log(m* m^2/n * m^3/n^2 * m^4/n^3 ... *m^n/n^n-1) 
  
=> log(m^(1+2+3+4+..+n)/n^(1+2+3+4+..+n-1) )
  
=> log[m^(n*(n+1)/2)/n^(n*(n-1)/2]

=>log[m^(n+1)/n^(n-1)]^n/2

so option should be D

Voting & Accepting an answer helps improve the community
← Previous · CAT 2003 | Question:...Next → · CAT 2003 | Question:...
← Previous in category · CAT 2003 | Question:...Next in category → · CAT 2003 | Question:...
Position:
Show:

Related questions

1 1 vote
1 1 answer
1.9k
1.9k views
go_editor asked May 5, 2016
1,947 views
CAT 2003 | Question: 2-93
If $\log_{10} x - \log_{10} \sqrt{x} = 2 \log_x 10$ then a possible value of $x$ is given by$10$$\frac{1}{100}$$\frac{1}{1000}$None of these
0 0 votes
1 answers 1 answer
1.7k
1.7k views
go_editor asked May 5, 2016
1,725 views
CAT 2003 | Question: 2-74
If $\frac{1}{3} \log_3 \text{M} + 3 \log_3 \text{N} =1 + \log_{0.008} 5$, then$\text{M}^9 = \frac{9}{\text{N}}$$\text{N}^9 = \frac{9}{\text{M}}$$\text{M}^3 = \frac{3}{\te...
1 1 vote
1 1 answer
1.7k
1.7k views
go_editor asked Mar 11, 2020
1,671 views
CAT 2016 | Question: 96
If $\log_{10}x-\log_{10}\sqrt x=2 \log_x10$, then a possible value of $x$ is given by$10$$1/100$$1/1000$None of these
1 1 vote
1 1 answer
1.8k
1.8k views
go_editor asked Mar 9, 2020
1,751 views
CAT 2015 | Question: 96
If $\log_{y}x=\left ( a \cdot \log_{z} y\right ) = \left ( b \cdot \log_{x}z \right )=ab,$ then which of the following pairs of values for $(a,b)$ is not possible?$(-2, 1...
0 0 votes
0 0 answers
2.2k
2.2k views
go_editor asked Feb 10, 2016
2,158 views
CAT 2003 | Question: 1-140
if $\log_3\left(2^x - 5\right), \: \log_3\left(2^x - \frac{7}{2}\right)$ are in arithmetic progression, then the value of $x$ is equal to$5$$4$$2$$3$