# 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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Expert Answers

hala718 | Certified Educator

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)

Student Comments

neela | Student

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.