How do you calculate #log_5 33# with a calculator?

1 Answer
Dec 12, 2016

Answer:

#log_5 33=2.1724#

Explanation:

The easiest way to solve such problems is to first change it to base #10#, as tables for base #10# are easily available. For this we can use the identity #log_b a=loga/logb#, where #loga# and #logb# are to base #10# (if base is not mentioned, it is taken as #10# and if base is #e#, we use #ln# - for natural logarithm).

Here, we have #log_5 33# and it is equal to #log33/log5# and from tables this is equal to

#1.5185/0.6990#

= #2.1724#

For using scientific calculator just press #5# and then button #log#, which gives #0.6990# (up to four places of decimals), now put this number in memory. Now press #33# and then button #log#, which gives #1.5185# up to four places of decimals. Now divide by memory recall (which has #0.6990# in memory) to get answer.