Question

I have a question on how my calculator handles logs, We all now that a log is kinda like the inverse of an exponent so to speak. and usually its written like 8=Log_2-3 but what is the calculator doing when type log 23 and thats it. and it spits out a decimal 1.36 what is that number .
We didnt specify a base or what we want it to equal
Any ideas

Answer 1

i got 1.36 when i type in log23 as well

Answer 2

your calculator has two logs, log base 10 and log base e
if you want to find a log to a different base, you have to use the change of base formula

Answer 3

so if you want
\[\log_{10}(50)\] then you can type that in directly and get the answer in one step

Answer 4

@satellite yea i get that but when you type just (LOG 23) what is it doing? its not log base 10 cuz that is not correct and its not LN cuz that is a seperate button

Answer 5

but if you want
\[\log_2(50)\] you have to type in
\[\frac{\log(50)}{\log(2)}\] do find it

Answer 6

\[\log(23)=1.3617...\] because
\[10^{1.3617...}=23\]

Answer 7

o so the "LOG" is automatically base 10 then

Answer 8

but if you want
\[\log_2(23)\] i.e. if you want to solve
\[2^x=23\] for x you have to enter
\[x=\frac{\log(23)}{\log(2)}\]

Answer 9

yes
"log" means
\[\log_{10}\]

Answer 10

similarly
\[\ln\] means
\[\log_e\]

Answer 11

ok that is what i was trying to figure out,
Thanks!

Answer 12

so for example
\[\log(1000)=3\] because
\[10^3=1000\]

Answer 13

yw

Answer 14

Log always means natural long to me unless it specifies log base 10

Answer 15

@zarkon log is log, but calculator ( pre ti 89) has log as a button, and that means
\[\log_{10}\]

Answer 16

natural long lol
log always mean log base 10 to me
and Ln means natural log

Answer 17

lol...oops

Answer 18

all logs are the same, just as all exponentials are the same. doesn't really matter what base is

Answer 19

that is why we should always use base e :)

Answer 20

that is why it never ceases to annoy me that math teachers want you to use the info given to write something as
\[A_0e^{kt}\] when
\[A_0 r^{\frac{t}{k}}\] would do just as well.

Answer 21

care loses 15% of its value each year. why in gods green earth am i supposed to write the model for the cars value as
\[A_0e^{kt}\] when i can use
\[A_0(.85)^t\]?

Answer 22

lol

Answer 23

for real. just because someone says i am supposed to use base e? and then due to rounding error i mess up all further calculations? makes no sense at all.