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Re: how to convert log
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.
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You need to find out what number x is 100%.
Start out with the facts known, 50 is 20% of this x, and write it down in mathematical symbols. This is just a translation of the words in your problem to the shortcut equation language used in math, the meaning is exactly the same, and with a little more experience you will easily move between these two.
50 = x * ( 20 / 100 )
Remember, 'percent' is from latin "per one hundred".
Multplying left and right side of the equation by 100 yields:
50 * 100 = x * ( 20 / 100 ) * 100, consolidation results in:
5000 = x * 20. Divide both sides by 20:
5000 / 20 = x * 20 / 20, consolidate:
250 = x.
In general you cannot. If the square root happens to be an integer (ex: SQRT (4)=2) or a rational number (SQRT(16/9)=4/3) you can convert from one form to the other, but that is the same as converting from a decimal to a fraction. However you can never convert 1.414213562 (the first 10 digits of SQRT(2)) into the radical SQRT(2). The reason is that root here is an irrational number: its decimal representation is endless and not periodic (non repeating).
Press Y= On the Y1 line enter the expression LOG(X+2)+LOG(X+3) by pressing LOG ALPHA [X] ) + LOG ALPHA [X] + 3 ) On the Y2 line enter the expression 7-X by pressing 7 - ALPHA [X] Press GRAPH to see the graph. To see where they intersect, press 2ND [CALC] 5. See "First curve?" in the lower left. Use up/down-arrow to select one of the two curves and press ENTER. See "Second curve?" in the lower left. Use up/down-arrow to select the other curve and press ENTER. See "Guess?" in the lower left. Press ENTER. The calculator will show the coordinates of the intersection.
Press MODE 4 to switch to the BASE-N mode. Enter the base-10 number and press =. Press SHIFT [BIN] (the LOG key) to switch to base-2 and see the result.
In general, once in the BASE-N mode, to convert a number from one base to another, switch the calculator into the first base using the keys in the third row, enter the number, press =, then switch the calculator into the second base.
This is not a calculator problem. Use the rules you have learned to simplify your problem. For a a log in any base. log(a*b) =log(a) +log(b) or log(a)+log(b) =log(a*b). Thus log(x+1)+log(x-2)= log[(x+1)*(x-2)]=1 Use the fact that log4=log in base 4 and rewrite the equation with the appropriate symbols. log4[(x+1)*(x-2)] =1 However 1=log4(4) and log4[(x+1)*(x-2)]=log4(4) The equality of the two logs implies the equality of their arguments (contents) and
Now you solve this quadratic equation by the methods you must have learned (sorry I have to leave some thing for you to do, to ensure that proper learning is achieved). Once you find the roots of the quadratic equation, verify that each term in your original expression has meaning-- x+1 positive and x-2 positive.
If one of the roots makes the argument (x+1) or (x-2) negative, reject it. because the argument of a log function cannot be negative.
Hello, There is no fraction button. Any division of two integers you do is represented as a decimal number. If you want your fraction to remain a fraction you enter it as follows 7[ / ] 19 [ MATH][1:ToFrac] [=] displays 7/19 If you want to convert a decimal number into a proper fraction press [MATH][1:ToFrac] . Exemple 7/19 [ENTER] gives .36842105. If without doing anything else, you press [MATH][1:ToFrac] you recover 7/19. There are limitations related to the number of decimal digits in the floating point number. .3684 [MATH][1:ToFrac][=] gives 921/2500 but .36842 [MATH][1:ToFrac][=] gives .36842 : it is not converted to fraction.