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CBSE Class 10 Answered

show that log162/343 +2log7/9 -log1/7=log 2
Asked by jchandhramouli88 | 22 Sep, 2020, 12:54: PM
answered-by-expert Expert Answer
To show that log162/343 +2log7/9 -log1/7=log 2

LHS equals log open parentheses 162 over 343 close parentheses plus 2 log open parentheses 7 over 9 close parentheses minus log open parentheses 1 over 7 close parentheses equals log open parentheses 162 over 343 close parentheses plus log open parentheses 7 over 9 close parentheses squared minus log open parentheses 1 over 7 close parentheses space space space... space open square brackets because space straight m space loga equals loga to the power of straight m close square brackets equals log open parentheses 162 over 343 close parentheses plus log open parentheses 49 over 81 close parentheses minus log open parentheses 1 over 7 close parentheses equals log open parentheses 162 over 343 cross times 49 over 81 close parentheses minus log open parentheses 1 over 7 close parentheses space space... space open square brackets because space loga plus logb equals log open parentheses ab close parentheses close square brackets equals log open parentheses 2 over 7 close parentheses minus log open parentheses 1 over 7 close parentheses equals log open parentheses fraction numerator begin display style 2 over 7 end style over denominator begin display style 1 over 7 end style end fraction close parentheses space space space space space space space space space space space space space space... space open square brackets because space loga minus logb equals log open parentheses straight a over straight b close parentheses close square brackets equals log 2 equals RHS

Hence, proved
Answered by Renu Varma | 22 Sep, 2020, 01:08: PM

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