Calculator question involving $\log_2$?

Question

I have a question, I have a calculator that does $\log$ but I think it does it it in a base ten format for example $\log_{10}(100)=2$ I am wondering how I can solve $\log$ using a base of 2 for example I know $2^7$ is $128$

so $\log_2(128)=7$

Is there any way find $\log$ using base of 2 by hand or some calculator method say I want to find what is $\log(100)$ using a base of two. How can I figure it out because my calculator a ti-83 does not let me.

Answer 1

$$ \log_2 x = \frac{\ln x}{\ln 2} = \frac{\log_{10} x}{\log_{10} 2}. $$ This is sometimes called the "change-of-base formula".

Answer 2

Yes, just use the fact that if you have a logarithm in base $b, \log_b(x)$, then you can convert it to base $a$ by $\frac{\log_b(x)}{\log_b(a)}$.

So, no matter what base your calculator uses, just divide $\ln(128)$ by $\ln(2)$, and you should get 7.