Question

log question?

Answer 1

sqrt{3} is the base ????

Answer 2

\(\large\color{black}{ \displaystyle \log_a(b)=\frac{\log_w(b)}{\log_w(a)}}\)

Answer 3

:P looks like \[\log_{\sqrt{3}} 13\]
\[\large\rm \log_a c = \frac{\log c}{\log a}\] change of base formula

Answer 4

You can change to any base w.

Answer 5

But, if you are using the calculator anyway, why would it make a difference if you change the base or not if you are still working via calculator?

Answer 6

I understand if you were doing it by hand. Painful, but possible if you know calculus. But I would assume this is not a by-hand calculus assignment.

Answer 7

No it's not. So what would be the next step?

Answer 8

\(\large\color{black}{ \displaystyle \log_a(b)=\frac{\log_{10}(b)}{\log_{10}(a)}}\)

Or, in your case,

\(\large\color{black}{ \displaystyle \log_\sqrt{3}(13)=\frac{\log_{10}(13)}{\log_{10}(\sqrt{3})}}\)

Answer 9

As possible:

\(\large\color{black}{ \displaystyle \log_\sqrt{3}(13)=\frac{\log_{10}(13)}{\log_{10}(\sqrt{3})}=\frac{\log_{10}(13)}{\log_{10}(3^{1/2})} \\[0.5em] \displaystyle =\frac{\log_{10}(13)}{(1/2)\log_{10}(3)}=\frac{2\log_{10}(13)}{\log_{10}(3)}}\)

Answer 10

then use calculator for top and bottom, but you can use the calculator right away.
http://www.wolframalpha.com/input/?i=log_%28%E2%88%9A3%29%2813%29

Answer 11

So 4.6694? Wow that site is so much better than mathway lol

Answer 12

That site is probably the most powerful, and the methematica.10 is like ridiculously awesome.