Alg9.4.49

From Exampleproblems

Jump to: navigation, search

Find the value of $\log_ a+\log_a a^2+\log_a (a^3)+...........\log_a(a^{2n-1})\,$ .

Applying logarithmic rule,

$1+a+a^2+a^3+.........+a^{2n-1}\,$

$\frac{n}{2}\cdot[2.1+(n-1)2]\,$

$\frac{n}{2}\cdot[2+2n-2]\,$

Hence

$\log_ a+\log_a a^2+\log_a (a^3)+...........\log_a(a^{2n-1})=n^2\,$ .

main Page:Algebra:Logarithmic

Retrieved from "http://www.exampleproblems.com/wiki/index.php/Alg9.4.49"

Views

Personal tools

Create an account or log in

Search

Toolbox

Argan Oil
Natural Skin Care
Organic Skin Care