If `(4^3)(4^6)(4^9)(4^(12))(4^(3x))=(0. 0625)^(-54)` , the value of `x` is 7 (b) 8 (c) 9 (d) 10

Explanation

Given,

`(4^3)(4^6)(4^9)(4^(12))(4^(3x))=(0. 0625)^(-54)`

`=>4^(3+6+9+12+....+3x)=((625)/(10000))^(−54)`

`=>4^3(1+2+3+4+.+x)=((1)/(16))^(-54)`

`=>4^((3(x(x+1)))/2)=(4^(−2))^(−54)`

Comparing both the sides :

`=>(3(x(x+1)))/2=108`

`=>x(x+1)=72`

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