How do you solve #log_10 30#?

1 Answer
Jan 21, 2016

Answer:

#1.4771#

Explanation:

You could just plug this into a calculator as #log30#.

Note that the #log# button on a calculator implies a base of #10#, so typing #log30# is the same as #log_10 30#.

This gives #log_10 30=1.4771#

Another way to simplify this is to write #30# as #10xx3#.

#log_10 30=log_10 ((10)3)#

Use log rules to expand this: #log_c(ab)=log_ca+log_cb#

#log_10 30=log_10 10+log_10 3#

Since #log_10 10=1#,

#log_10 30=1+log_10 3#