Logarithmic arithmetic progression

Terms involve logarithms; use log laws to show the sequence is arithmetic or find parameters.

1 questions · Moderate -0.8

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OCR MEI Paper 1 2023 June Q14
6 marks Moderate -0.8
14
  1. 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 \(\log _ { 10 } 20 , \log _ { 10 } 200 , \log _ { 10 } 2000\).
  2. Show that the sequence is arithmetic.
  3. Find the exact value of the sum of the first 50 terms of this sequence.