recategorized
714 views
3 votes
3 votes
What is the value of $\{ ( 1/ \log_3 60)+ (1/ \log_4 60 ) + (1/ \log_5 60) \}$?
  1. $0$
  2. $1$
  3. $5$
  4. $60$
recategorized

2 Answers

5 votes
5 votes

we know that $\log_b a = 1/ log_a b$

So $1/log_3\ 60 + 1/log_4\ 60 + 1/log_4\ 60$

$= log_{60}\ 3 + log_{60}\ 4 + log_{60}\ 5$

$= log_{60}\ 3*4*5$              ($\because log_d\ a + log_d\ b + log_d\ c = log_d\ a*b*c$)

$= log_{60}\ 60$

$= 1$

edited by
1 votes
1 votes

$\frac{1}{log_{3}60}+\frac{1}{log_{4}60}+\frac{1}{log_{5}60}$

=$\frac{1}{log_{3}3+log_{3}4+log_{3}5}+\frac{1}{log_{4}3+log_{4}4+log_{4}5}+\frac{1}{log_{5}3+log_{5}4+log_{5}5}$

=$\frac{1}{1+log_{3}4+log_{3}5}+\frac{1}{log_{4}3+1+log_{4}5}+\frac{1}{log_{5}3+log_{5}4+1}$

=$\frac{1}{1+\frac{log4}{log3}+\frac{log5}{log3}}+\frac{1}{\frac{log3}{log4}+1+\frac{log5}{log4}}+\frac{1}{\frac{log3}{log5}+\frac{log4}{log5}+1}$

=$\frac{log3}{log3+log4+log5}+\frac{log4}{log3+log4+log5}+\frac{log5}{log3+log4+log5}$

=$\frac{log3+log4+log5}{log3+log4+log5}$

=$1$

Option B.

Answer:

Related questions

3 votes
3 votes
2 answers
1
Ruturaj Mohanty asked Dec 27, 2018
735 views
If $a/b=c/d$, then which of the following does not hold good?$(a+b)/b=(c+d)/d$$(a+c)/(b+d)=(a-c)/(b-d)$$(a+b)/(a-b)=(c+d)/(c-d)$$(a+c)/(b-d)=(a-c)(b+d)$
4 votes
4 votes
1 answer
2
Ruturaj Mohanty asked Dec 27, 2018
4,609 views
$N$ is the smallest number that has $5$ factors. How many factors does $N-1$ have?$4$$6$$5$$3$
3 votes
3 votes
4 answers
3
Ruturaj Mohanty asked Dec 27, 2018
876 views
What is the value of $(x \% \text{ of } y) + (y \% \text{ of } x)$?$20 \% \text{ of } x/y$$2 \% \text{ of } x/y$$2 \% \text{ of } xy$$20 \% \text{ of } xy$
4 votes
4 votes
2 answers
4
Ruturaj Mohanty asked Dec 27, 2018
3,175 views
A book contains $100$ pages. A page is chosen at random. What is the chance that the sum of the digits on the page is equal to $8$?$0.08$$0.09$$0.90$$0.10$