How do you calculate #log_6 53# with a calculator?

1 Answer
Aug 19, 2016

Answer:

#x = 2.216#

Explanation:

Some calculators can do log calculations with bases other than 10.
However, let's assume that we have a calculator which only has log with base 10.

Let # log_6 53 = x" write in index form"#

#6^x = 53" find log of both sides"#

#log6^x = log53#

#xlog6 = log53#

#x = log_10 53/log_10 6#

This is the same result as using the change of base rule.

#x = 2.216#