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If (4)^(a+5) (16) ^(2a)(32)^(4)=(16)^(3a...

If `(4)^(a+5) (16) ^(2a)(32)^(4)=(16)^(3a)`then a =___

A

15

B

30

C

24

D

20

Text Solution

Verified by Experts

The correct Answer is:
A
Given,
`(4)^(a+5)xx (16) ^(2a)xx(32)^(4)=(16)^(3a)`
`rArr(2^2)^(a+5)xx (2^4) ^(2a)xx(2^5)^(4)=(2^4)^(3a)`
`rArr(2)^(2a+10)xx (2^(8a))xx2^20=2^12a`
`rArr (2)^(2a+10+8a+20)=(2)^(12a)`
`rArr (2)^(10a+30)=(2)^(12a)`
`rArr10a +30a=12a`
`rArr2a=30`
`rArra=15`
Hence,the correct option is (a).
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