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Find the value of the following: (i) ...

Find the value of the following:
(i) ` log_(10) 2 + log_(10) 5`
(ii) ` log_(3) (sqrt(11)-sqrt2) + log_(3) (sqrt11+sqrt2)`
(iii) ` log_(7) 35 - log_(7) 5`

Text Solution

Verified by Experts

(i) `log_(10)2+ log_(10) 5 = log_(10)(2 xx 5)= log_(10) 10 = 1`
`(ii) log_(3)(sqrt11-sqrt2)+log_(3)(sqrt11+sqrt2)`
` " "= log_(3) (sqrt11-sqrt2) xx (sqrt11+sqrt2)`
`" "= log_(3) (11-2)=log_(3)9=2 (as 3^(2) = 9)`
`(iii) log_(7)35-log_(7) 5 = log _(7). 35/5 = log_(7) 7 = 1`
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