Regarding learning curve

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How to calculate log40 value,if log2 & log5 value given.... As the question given ln practice manual .... I mean the logic behind the 3*log2+log5....plz help me..

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find the multiples of 40 i.e 40 can be written as 5X8.

 

Then 8 can be written as 23 i.e 2 cube(2X2X2)

as per logarthms formulae

log abc can be written as Loga + Log b+ Log c

and Logab  = b log a

 

in this formulae if you substitute

log 40 = log 8 + log 5

            = log 23 (2 cube) + log 5

= 3 log 2 + log 5

Giving values of log 2 and log 5 we will get answer

 

Thanks a lot Madhavi

 

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