Question #e40f1

1 Answer
Aug 23, 2016

#sum_(i=1)^n ln(a_i) = ln(prod_(i=1)^n a_i)#

Explanation:

The trick here is to remember that logarithms have the property

#log_b(x)+log_b(y)=log_b(xy)#

Then, if we have a sum of logarithms, we can combine the terms into a single logarithm of the product of the arguments of the original logarithms:

#sum_(i=1)^n log_b(a_i) = log_b(prod_(i=1)^n a_i)#

Applying that to the given case:

#sum_(k=10)^14ln(k) = ln(10*11*12*13*14)=ln(240240)~~12.39#