How do you use a calculator to evaluate the expression #log2.3# to four decimal places?

1 Answer
Oct 13, 2016

Answer:

It will depend upon your calculator and its built-in functions.
(see below for two examples)

#log 2.3 ~~0.3617#

Explanation:

First Calculator from my desk drawer: Sharp EL-5400
I notice that this calculator has a "log" key,
so I punch in: #2.3#
and then the "log" key.
Display shows #0.361727836#
which I round/truncate to #0.3617# to meet the four decimal place requirement.

Second Calculator from my desk drawer: TI BA II Plus*
I don't see a "log" button, but I do have a "ln" button
so I will need to use the change of base formula:
#color(white)("XXX")log_10 2.3 = (log_e 2.3)/(log_e 10)#
(remember default base for #log# is #10# and #ln=log_e#)

To evaluate #log_e 10#:
#color(white)("XXX")#I punched in: #10#
#color(white)("XXX")#then "ln"
#color(white)("XXXXXX")#Display showed #2.30259#
#color(white)("XXX")#I hit "STO# to store this value.

To evaluate #log_E 2.3#
#color(white)("XXX")#I punched in: #2.3#
#color(white)("XXX")#then "ln"
#color(white)("XXXXXXX")#Display showed #083291#

To find #log_10 2.3#
#color(white)("XXX")#I punched #div#
#color(white)("XXX")#then "RCL"
#color(white)("XXX")#then #=#
#color(white)("XXXXXXX")#Display showed #0.36173#