Q 10 If log2log2log3x=log2log3log2y=0 then the value of (x + y) is: (a) 17 (b) 9 (c) 21 (d) - Maths - Integrals

Question

Q 10 If log 2 log 2 log 3 x = log 2 log 3 log 2 y = 0 then the
value of (x + y) is:
(a) 17
(b) 9
(c) 21
(d) 19

Shruti Tyagi · Accepted Answer

Dear student,

We have,log2log2log3x=log2log3log2y=0Taking antilog i
e
 logba=x ⇒bx=a⇒log2log3x=log3log2y=20⇒log2log3x=log3log2y=1                 --[using a0=1]taking log2log3x=1Again taking antilog log3x=2again taking antilog⇒x=32⇒x=9taking log3log2y=1Taking antilog log2y=31⇒log2y=3again taking antilog⇒y=23⇒y=8Now, x+y=9+8=17thus option a is correct
Regards

Q.10. If log 2 log 2 log 3 x = log 2 log 3 log 2 y = 0 then the value of (x + y) is: (a) 17 (b) 9 (c) 21 (d) 19

Q.10. If $\log_{2} (\log_{2} (\log_{3} x)) = \log_{2} (\log_{3} (\log_{2} y)) = 0$ then the value of (x + y) is:
(a) 17
(b) 9
(c) 21
(d) 19