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If (4^3)(4^6)(4^9)(4^(12))(4^(3x))=(0. 0...

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

Text Solution

Verified by Experts

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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Knowledge Check

  • If 9^(8.6)xx8^(3.9)xx72^(4.4)xx9^(3.9)xx8^(8.6)=72^(x) , then value of x is

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    B
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