
Example: Show that, log 55125 = 2 log 7 + 3 log 5 + 2 log 3. Solution: Given that, RHS = Log 55125 Take the factors of 55125, we get 55125 = 5 * 11025 = 5 * 5 * 2205 = 5 * 5 * 5 * 441 = 5 * 5 * 5 * 3 * 147 = 5 * 5 * 5 * 3 * 3 * 49 = 5 * 5 * 5 * 3 * 3 * 7 * 7 55125 = 5^{3} * 3^{2} * 7^{2} Taking log on both sides log 55125 = log (5^{3} * 3^{2} * 7^{2}) = log 5^{3} + log 3^{2} + log 7^{2} = 3 log 5 + 2 log 3 + 2 log 7 Therefore log 55125 = 2 log 7 + 3 log 5 + 2 log 3. Hence proved the given problem. Directions: Prove the following problems. Also write at least ten examples of your own. Show that, log 9000 = 3 log 2 + 2 log 3 + 3 log 5. Show that, log 741125 = 3 log 5 + 2 log 7 + 7 log 11. Show that, log 8575 = 3 log 7 + 2 log 5. Show that, log 605 = log 5 + 2 log 11. Show that, log 2025 = 4 log 3 + 2 log 5.
Show that, log 1323 = 3 log 3 + 2 log 7. 