How do you calculate #log_7 5.8# with a calculator?

1 Answer
Aug 9, 2016

Answer:

#log_7 5.8 = (log_10 5.8)/(log_10 7) = 0.9034#

Explanation:

Some calculators are able to calculate logs with any base, but let's work through this for those calculators which can only work with base 10.

Let # log_7 5.8 = x" log form"#

#7^x = 5.8" index form"#

The variable is in the index, find the log of both sides.

#log_10 7^x = log_10 5.8#

#xlog_10 7 = log_10 5.8#

#x = (log_10 5.8)/(log_10 7)#

Now use a calculator to find the answer #0.9034#

#log_a b = (log_10 b)/(log_10 a) " is called the change of base law"#

We could have written the following in one step:

#log_7 5.8 = (log_10 5.8)/(log_10 7) #