Question

can log

Answer 1

\[\log_{5} 8 = \ln 8 / \ln 5\]

Answer 2

are they equalivent

Answer 3

yup

Answer 4

100% @OOOPS ? it can also be rewritten as log8/log5 right?

Answer 5

yup again and 100%

Answer 6

you can check by hitting your calculator. hit ln, then hit log with ANY BASE. As long as you hit the same base on log, you are ok. I mean ln / ln , log_3/ log_3. DON'T PUT ln/ log_3.

Answer 7

\[\ln x = \log_e x = \frac{\log x}{\log e} \]So,\[\frac{\ln 8}{\ln 5} = \frac{\frac{\log 8}{\log e}}{\frac{\log 5}{\log e}} = \frac{\log 8}{\log e}\times \frac{log e}{\log 5} = \frac{\log 8}{\log 5} = log_5 8\]

Answer 8

What you need to know is \(\log_ab = \frac{log b}{log a}\)

Answer 9

$$\Large \frac{\log_{~a} 8}{ \log_{~a} 5 }= \frac{\ln 8 }{\ln 5}=\frac{\log_{~10} 8}{ \log_{~10} 5 } $$

Answer 10

just double checking, you use log to mean log base 10

Answer 11

i have seen log by itself to mean log base e, sorry i dont mean to confuse the OP

Answer 12

Now, this is complicated. It can be of base 10, base 2, base 100000, or base k, for some (real?!) numbers k.
Would be better to write the identity as \(\large \log_a b = \frac{\log_kb}{\log_k a}\)

Yes, when I took a math course organized by engineering department, my professor wrote log instead of ln for log base e. He said in advanced mathematics, we used natural log instead of common log, and log in our course means ln.

Answer 13

the only restriction here, k > 0

Answer 14

does a negative base make sense

Answer 15

a positive real number which is not equal to 1

Answer 16

that makes sense, since 1 to any power stays 1. thank you for clarifying

Answer 17

np :) Thanks too for your questions!