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#

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