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Re: I need help with a change of base formula problem.
It's simple here some logs:
log x base y = log x / log y
log (x*y) = log x + log y
log (x/y) = log x - log y you just need to know that the default base of log in calculators is 10, so log x mean log x base 10 = log x / log 10, so write log x / log y for log x base y example: log 8 base 2 = log 8 / log 2 that is how you write it on calculator, hope it was helpful
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The Casio FX-300MS does not provide base 2 logarithms as a single key operation. However, you can use the natural logarithm (ln, base e = 2.7182818...) and the formula
log2 ( x ) = ln( x ) / ln( 2 )
To calculate the base 2 logarithm of 16, key in
[ln] 16 [/] [ln] 2 [=]
and get displayed the correct answer 4.
The same simple formula also works for any other base, and actually for any other logarithms provided by your calculator. The FX-300MS also provides a logarithm to base 10 (lg). You could also
[lg] 16 [/] [lg] 2 [=] to get the solution to the problem above, or
[lg] 25 [/] [lg] 5 [=] to get the base 5 logarithm of 25.
The TI 86 has two logarithmic functions: natural logarithm (ln) and common (decimal) logarithms (log). If you need the logarithm in any other base than e or 10 you need to use one of the two equivalent expressions log_b(x) =ln(x)/ln(b) =log(x)/log(b) Here b is the value of the base of the logarithm and x is the argument (the value whose logarithm you are seeking). Of course the argument x must be a positive number. Note: On the TI 86 the log function can calculate the logarithm of a complex number, according to the manual.
I am not sure there is a question expressed here. If you have a formula you want to use to calculate some quantity in it, state the formula, provide the known values and we will show you how to enter it. As to what it serves for, I for one do not need to know.
Using logarithms. For example, if A ^ X = 2; then X = logA(2);
This calculator only works in base-10 logarithms or natural logarithms, you should use the base conversion formula.
logA(X) = logC(X) / logC(A).
To calculate the common log ( LOG base 10) of a positive number, just press the LOG key, the one above the blue Division key, then enter the number and close the right parenthesis. Press the ENTER key to get the result.
If you want to calculate the log in a base other than e (natural) or 10 (decimal) logarithms, you need to make use of one of the equivalent formulas below
log in base a of a number b log_a(b)=log_10(b) / [ log_10(a)] or log_a(b)= ln(b)/ln(a)
Your calculator knows only the decimal logarithms log or log_10 and the natural logarithms (ln or log in base e). So you cannot compute directly the logarithms in any bases other than 10 and e. A workaround consists in using the relation log in base b of a number a (log_b (a)) log_b(a)= (log_10(a) ) / (log_10 (b)) or the relation log_b(a)= ln(a)/ln(b)
log_2(0.3)=log(0.3)/log(2) where log is log in base 10 Similarly log_2(0.3)=ln(0.3)/ln(2) As to the multiplicative factor you had at the beginning of your expression, just multiply the value obtained by one on the formulas above (both formulas will give the same result) by 0.3
For natural logarithms Press [2nd][X], enter a positive number, close the right parenthesis and press [ENTER]. If the number is decimal the result is displayed as a number. If the number is integer, put a decimal mark at its end to have the result displayed as decimal.
For decimal logarithms use the ALPHA keyboard to enter the log( command, complete the argument and press ENTER
If you want to calculate log in base a of number b type log(b,a).
Your calculator cannot compute directly the logarithms in an arbitrary base, but you have the means to obtain that indirectly.
You can use either of the conversion formulas shown on the screen capture (on the right). On screen capture ln stands for natural logarithm.
If you want binary logarithms (logs in base 2) you use the relation log_2 (x) =ln(x)/ln(2)
Use whichever formula is shorter to key in (without pressing the 2nd key).
(from Wikipedia - the proof also follows if you want to go look it up)
While there are several useful identities, the most important for calculator use lets one find logarithms with bases other than those built into the calculator (usually loge and log10). To find a logarithm with base b, using any other base k:
Hello, You are victim of a confusion between terms. Base-n calculations are calculations using various numeration systems (bases) : binary (2), octal(8) hexadecimal (16) and decimal (10). What you want is how to calculate powers, logarithms, exponentials and these have also the notion of base; Log in base 10 is the common log, whereas natural logarithms, are logarithms in base e. Back to your exemple: 5 times 5 and raise the whole to power 3? In that case [(] 5 [x] 5 [)] [^] 3 or [X to the 3] if you have such key or 25 [^] 3, because 5x5 = 25
5 times (5 raised to power 3) 5[x] [( ] 5 [^] 3 [)] or 5 [^] 4 because of the rules about products of powers with the same base.