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If (21. 4)^a=(0. 00214)^b=100 , then the...

If `(21. 4)^a=(0. 00214)^b=100` , then the value of `1/a-1/b` is 0 (b) 1 (c) 2 (d) 4

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`(21.4)^a=100-(1)`
`0.00214=21.4*10^(-4)`
`(21.4*10^(-4))^10=100-(2)`
`alog(2.14)=2`
`blog(21.4*10^(-4))=2`
`b[log21.4+log10^(-4)]=2`
`b[log21.4-4]=2`
`b[2/a-4]=2`
...
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