1.

the value of `log_7 [log_7 sqrt(7sqrt(7sqrt7))]` isA. `3 log_(2)7`B. `1-3log_(2)7`C. `1-3log_(7)2`D. `(7)/(8)`

Answer» Correct Answer - C
Let `log_(7)log_(7)sqrt(7sqrt(7sqrt(7)))=x`
`"then "7^(x)=log_(7)sqrt(7sqrt(7sqrt(7)))`
`7^(x)=(1)/(2).log_(7)7sqrt(7sqrt(7))`
`7^(x)=(1)/(2)[log_(7)7+(1)/(2)log_(7)7sqrt(7)]`
`=(1)/(2)[1+(1)/(2)log_(7)7+(1)/(2)log_(7)sqrt(7)]`
`=(1)/(2)[1+(1)/(2)+(1)/(4)]`
`7^(x)=(7)/(8)`
`x=log_(7)((7)/(8))`
`x=log_(7)7-log_(7)8`
`x=1-3log_(7)2" "(becauselog_(7)8=log_(7)2^(3))`


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