CAT Exam Model Paper 8 with solutions for free online practice

Question : 21 of 60

Marks: +1, -0

[log(1)+log(1+3)+log(1+3+5)+...log(1+3+5+...+19) -2[log1 + log2 + ...log7] = m +nx + ay If log2 = x and log3 = y
then which of the following is the ordered triplet (m, n, a)?
[Note: Use Base 10 for all the logarithmic functions.]

(2, 6, 4)
(2, 7, 4)
(2,4,7)
(2,4, 6)

Validate

Solution:

(log1 + log4 + log9 +.... + log100 )

- 2∑↖{7}↙{\i=1} \log \i

= 2log10! -2log7!
= 2log

10!/7!

= 2log720
= 2[log

(10×9×8)

]
= 2[1 + 3log2 + 2log3]
= 2[1 + 3x + 2y] = 2 + 6x + 4y
So 2 + 6x + 4y = m + nx + ay
∴ (m, n, a) = (2, 6, 4)

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