log(6/11)^5 how do you expand that

5 * log ( 6 / 11 ) = 5 * ( log6 - log11 ) = 5 * [ log(2 * 3) - log11] = 5 * (log2 + log3 - log11 ).

Answered by crisforp | 2024-06-10

We know that C log a = log a^C. We know that log (x/y) = log x - log y We know that log xy = log x + log y Therefore... log(6/11)^5 = 5 * log (6/11). Which can be expanded to... 5 (log 6 - log 11) ... 5 (log 3 + log 2 - log 11)
Its a law of logarithms.

Answered by maxaustein | 2024-06-10

To expand lo g ( 11 6 ​ ) 5 , use the Power Rule to get 5 ⋅ lo g ( 11 6 ​ ) and then apply the Quotient Rule to result in 5 ⋅ lo g ( 6 ) − 5 ⋅ lo g ( 11 ) .
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Answered by crisforp | 2024-09-27