How to convert log

Hello, The first remark is this. The ratio log(0.8)/log(2) is by definition binary log of 0.8 ( meanibg log in base 2 of 0.8) The second remark is good news for you.: When in MathIO, [SHIFT][MODE][1:MathI0], your calculator can compute directly the log in any base of any number. To use the functionality, you press the key below [ON]. It is a log symbols with a small solid square, and and erect empty rectangle.
When you press the key the screen shos a template. In the smaller and lowered square goes the base (here 2). When you enter the base, press the right arrow to move cursor to the rectangle inside the parentheses and type in 0.8. Use the right arrow to move the cursor out of the parentheses.
Practice: try that. the result should be -0.321928095. Good. Now use the replay button to move cursor to the command line outside the right parenthesis. I am going to give you the other key stokes. Let log(2,0.8) be my representation for log in base2 of 0.8. Then you enter the rest of the calculation as
log(2, 0.8) [*] [ ( ] [(-)] 0.321 [ ) ] [*] 2500 [=]
Here [*] is the multiplication sign [(-)] is the negation (change sign), just above the [RCL] key.
[ ( ] is the left parenthesis and [ ) ] its matching right parenthesis. Both of them enclose the number -0.321. It underlined them for clarity.
The result should be 259.0716344
If you do not like what I did above, you can always do things the old way. You use the log key just above the [COS] key. In that case -0.3219*[LOG] (0.80)/[LOG] 2 * 2500. Do not to supply the ) for both log. The calculator inserts the left ones by default.
Hope it helps.