Question

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

Answer 1

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`