Math, asked by aryanppp, 1 year ago

please solve with correct method.....

rakeshmohata: answer is 1

rakeshmohata: that's option c

aryanppp: yeah but how?

aryanppp: please solve it...

rakeshmohata: log 2 base 2 = 1

rakeshmohata: no option for answering!

aryanppp: but there are log 2 base 2 three times

rakeshmohata: hmm and log aⁿ = n log a

aryanppp: and two logs will become one but third one will remain log 4 base 2

Answers

Answered by rakeshmohata

Hope u like my process
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Formula to be used
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$= > log_{a}(a) = 1 \\ \\ = > log( {x}^{y} ) = y log(x)$
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$= > \bf \: log_{2}( log_{2}( log_{2}(16) ) ) \\ \\ = log_{2}( log_{2}( log_{2}( {2}^{4} ) ) ) \\ \\ = log_{2}( log_{2}(4 log_{2}(2) ) ) \\ \\ = log_{2}( log_{2}(4) ) \\ \\ = log_{2}( log_{ {2} }( {2}^{2} ) ) \\ \\ = log_{2}(2 log_{2}(2) ) \\ \\ = log_{2}(2) = \bf \underline{1}$
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Hope this is ur required answer

Proud to help you

rakeshmohata: thanks for the brainliest one

Answered by MrVk

hey , 16 can be written as 2^4 where 4 will come front and log 2 base 2 is 1 and again 4 can be written as 2^2 and again 2 will come front and log 2 base 2 will be 1 and one will be left that is log 2 base 2 , again it will be 1 and therefore final answer will be 1

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