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

Oct 13, 2016

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

$\log 2.3 \approx 0.3617$

#### 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:
$\textcolor{w h i t e}{\text{XXX}} {\log}_{10} 2.3 = \frac{{\log}_{e} 2.3}{{\log}_{e} 10}$
(remember default base for $\log$ is $10$ and $\ln = {\log}_{e}$)

To evaluate ${\log}_{e} 10$:
$\textcolor{w h i t e}{\text{XXX}}$I punched in: $10$
$\textcolor{w h i t e}{\text{XXX}}$then "ln"
$\textcolor{w h i t e}{\text{XXXXXX}}$Display showed $2.30259$
$\textcolor{w h i t e}{\text{XXX}}$I hit "STO# to store this value.

To evaluate ${\log}_{E} 2.3$
$\textcolor{w h i t e}{\text{XXX}}$I punched in: $2.3$
$\textcolor{w h i t e}{\text{XXX}}$then "ln"
$\textcolor{w h i t e}{\text{XXXXXXX}}$Display showed $083291$

To find ${\log}_{10} 2.3$
$\textcolor{w h i t e}{\text{XXX}}$I punched $\div$
$\textcolor{w h i t e}{\text{XXX}}$then "RCL"
$\textcolor{w h i t e}{\text{XXX}}$then $=$
$\textcolor{w h i t e}{\text{XXXXXXX}}$Display showed $0.36173$