Iflog3log(3x−2)andlog(3x+4)areinarithmeticprogression,thenxisequalto−Iflog3log(3x−2)andlog(3x+4)areinarithmeticprogression,thenxisequalto−\eqalign{
& {\text{If}}\,\log 3\log \left( {{3^x} - 2} \right)\,{\text{and}}\,\log \left( {{3^x} + 4} \right)\, \cr
& {\text{are}}\,{\text{in}}\,{\text{arithmetic}}\,\,{\text{progression}}\,{\text{,}} \cr
& {\text{then}}\,x\,{\text{is}}\,{\text{equal}}\,{\text{to}} - \cr} " />
Iflog3log(3x−2)andlog(3x+4)areinarithmeticprogression,thenxisequalto−Iflog3log(3x−2)andlog(3x+4)areinarithmeticprogression,thenxisequalto−\eqalign{
& {\text{If}}\,\log 3\log \left( {{3^x} - 2} \right)\,{\text{and}}\,\log \left( {{3^x} + 4} \right)\, \cr
& {\text{are}}\,{\text{in}}\,{\text{arithmetic}}\,\,{\text{progression}}\,{\text{,}} \cr
& {\text{then}}\,x\,{\text{is}}\,{\text{equal}}\,{\text{to}} - \cr} " />
Iflog3log(3x−2)andlog(3x+4)areinarithmeticprogression,thenxisequalto−Iflog3log(3x−2)andlog(3x+4)areinarithmeticprogression,thenxisequalto−\eqalign{
& {\text{If}}\,\log 3\log \left( {{3^x} - 2} \right)\,{\text{and}}\,\log \left( {{3^x} + 4} \right)\, \cr
& {\text{are}}\,{\text{in}}\,{\text{arithmetic}}\,\,{\text{progression}}\,{\text{,}} \cr
& {\text{then}}\,x\,{\text{is}}\,{\text{equal}}\,{\text{to}} - \cr} " />
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",
"text": "If log 3 log ( 3 x − 2 ) and log ( 3 x + 4 ) are in arithmetic progression , then x is equal to − If log 3 log ( 3 x − 2 ) and log ( 3 x + 4 ) are in arithmetic progression , then x is equal to −
",
"dateCreated": "7/24/2019 10:09:12 AM",
"author": {
"@type": "Person",
"name": "Nitin Sir"
},
"answerCount": "4",
"acceptedAnswer": {
"@type": "Answer",
"text": "
Solution:
In arithmetic progression common ratio are equal to log ( 3 x − 2 ) − log 3 = log ( 3 x + 4 ) − log ( 3 x − 2 ) = log ( 3 x − 2 ) log 3 = log ( 3 x + 4 ) log ( 3 x − 2 ) ( ∴ log a − log b = log a b ) = log 3 x log 2 log 3 = x log 3 log 4 log 2 x log 3 = x log 3 log 2 log 3 = x log 3 log 4 log 2 x log 2 = x log 2 = log 4 log 2 ⇒ x = log 4 log 2 log 2 ⇒ x = log 8 ⇒ x = log 2 3 In arithmetic progression common ratio are equal to log ( 3 x − 2 ) − log 3 = log ( 3 x + 4 ) − log ( 3 x − 2 ) = log ( 3 x − 2 ) log 3 = log ( 3 x + 4 ) log ( 3 x − 2 ) ( ∴ log a − log b = log a b ) = log 3 x log 2 log 3 = x log 3 log 4 log 2 x log 3 = x log 3 log 2 log 3 = x log 3 log 4 log 2 x log 2 = x log 2 = log 4 log 2 ⇒ x = log 4 log 2 log 2 ⇒ x = log 8 ⇒ x = log 2 3
",
"dateCreated": "7/24/2019 10:09:12 AM",
"author": {
"@type": "Person",
"name": "Nitin Sir"
}
},
"suggestedAnswer": {
"@type": "Answer",
"text": "
Solution:
In arithmetic progression common ratio are equal to log ( 3 x − 2 ) − log 3 = log ( 3 x + 4 ) − log ( 3 x − 2 ) = log ( 3 x − 2 ) log 3 = log ( 3 x + 4 ) log ( 3 x − 2 ) ( ∴ log a − log b = log a b ) = log 3 x log 2 log 3 = x log 3 log 4 log 2 x log 3 = x log 3 log 2 log 3 = x log 3 log 4 log 2 x log 2 = x log 2 = log 4 log 2 ⇒ x = log 4 log 2 log 2 ⇒ x = log 8 ⇒ x = log 2 3 In arithmetic progression common ratio are equal to log ( 3 x − 2 ) − log 3 = log ( 3 x + 4 ) − log ( 3 x − 2 ) = log ( 3 x − 2 ) log 3 = log ( 3 x + 4 ) log ( 3 x − 2 ) ( ∴ log a − log b = log a b ) = log 3 x log 2 log 3 = x log 3 log 4 log 2 x log 3 = x log 3 log 2 log 3 = x log 3 log 4 log 2 x log 2 = x log 2 = log 4 log 2 ⇒ x = log 4 log 2 log 2 ⇒ x = log 8 ⇒ x = log 2 3
",
"dateCreated": "7/24/2019 10:09:12 AM"
}
}
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