cat 2021 Question 6

Question

For a real number a, if $\frac{\log _{15} a+\log _{32} a}{\left(\log _{15} a\right)\left(\log _{32} a\right)}=$ = 4 then a must lie in the range

Accepted Answer

$\frac { \log _ { 15 } ^ { a } + \log _ { 32 } ^ { a } } { \left( \log _ { 15 } ^ { a } imes \log _ { 32 } ^ { a } ight) }$ = 4

we get $\log⁡_a$(log⁡ 32 + log⁡ 15) = 4(log⁡ a$)^2$

we get (log⁡ 32 +log⁡ 15)=4log⁡a

= log⁡480 = $log⁡ a^4$

= $a^4$ = $480$

so we can say a is between 4 and 5 .

Question 6.