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Online Quiz (Worksheet A B C D)

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High School Mathematics
3.22 Problems on Logarithms - II

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 = 53 * 32 * 72
Taking log on both sides
log 55125 = log (53 * 32 * 72)
= log 53 + log 32 + log 72
= 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.

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