Question

Question #e40f1

Answer 1

`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`