Find the logarithm: log10(2sqrt6) Both 10 and 2 are exponents..10 is below the log and 2 is above but before the sqrt

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

log 10 (2sqrt6)

 = log 10 (2)(6)^1/2

We know that log xy = logx + log y

==> log 10 (2)(6)^1/2 = log 10 (2) + log 10 (6)^1/2

           = log 10 (2)+ (1/2)log 10 (6)

           = log (2)+ (1/2) log 10 (2)(3)

           = log (2) + (1/2)log 10 (2) + (1/2)log 10 (3)

           = (3/2)log 10 (2) + (1/2)log 10 (3)

           = (3/2)*(0.3) + (1/2)* (0.48)

            = 0.69 (approximately)

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

Hope you mean to find log (10^2sqrt6)

Solution:

ln  said of logarithm to the base e and log is normally notation for the logarithm to the base 10. So,

let  log 10^(2sqrt 6) = x .Taking antilologarithms,

10^(2log6) = 10^x. Since the base on both sides are same the powers should be equal. So,

x = 2sqrt 6  = 4.89898 nearly.

 

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