Use the laws of logarithms to show that \(\log _ { 10 } 200 - \log _ { 10 } 20\) is equal to 1 .
The first three terms of a sequence are \(\log _ { 10 } 20 , \log _ { 10 } 200 , \log _ { 10 } 2000\).
Show that the sequence is arithmetic.
Find the exact value of the sum of the first 50 terms of this sequence.