Solve lg 12 lg 23 lg 34 lg 99100 Solutionlg12lg23lg34lg

Solve lg 1/2 + lg 2/3 + lg 3/4 + ... + lg 99/100 .

Solution

lg1/2+lg2/3+lg3/4+....+lg99/100.

We know lga+lgb = lgab. We use this to solve the above.

lg1/2+lg2/3+lg3/4 +....99/100= lg{(1/2)(2/3)(3/4)(4/5).....(98/99)(99/100)}

= lg (1/100)

= lg1-lg100

=0-2

=-2.

Therefore lg 1/2 + lg 2/3 + lg 3/4 + ... + lg 99/100 = -2.