How do you calculate #log_5 7.2# with a calculator?

1 Answer
Gió
Aug 9, 2016

I found: #1.22656#

Explanation:

Normally in a calculator you have two types of logs: one in base #e# and the other in base #10#.
Our log is in base #5# but it isn't a problem because we can change base using the relationship:

#log_a(x)=(log_(10)x)/(log_(10)a)#

where we used the new base #10# that can be evaluated.

In our case we get:

#log_5(7.2)=(log_(10)(7.2))/(log_(10)(5))=1.22656#

Related questions
See all questions in Functions with Base b
Impact of this question
1363 views around the world
You can reuse this answer
Creative Commons License