SOLUTION: how do you enter logrithmic expressions into the calculator with subscripts

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Question 276828: how do you enter logrithmic expressions into the calculator with subscripts
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Short answer: You can't (at least not directly).

Pretty much any calculator that can do logarithms at all can do base 10 logarithms. And many of those can also do base e (ln) logarithms. I have never seen a calculator that can do logarithms of any other base.

Since the subscripts you see are the bases of the logarithms, any logarithm with a subscript/base different from 10 or e cannot be done (directly) on a calculator.

So how do we find logarithms of bases other than 10 or e? Answer: Use the change of base formula to convert the logarithm you have into an expression of base 10 (or base e) logarithms. The change of base formula for logarithms is: log%28a%2C+%28x%29%29+=+log%28b%2C+%28x%29%29%2Flog%28b%2C+%28a%29%29.

Here's an example. The first step is using the change of base formula:

or


Note #1: See how the answer works out the same whether you use base 10 logarithms or base e (ln) logarithms. Even though the individual logarithms in the fraction are different, the quotient works out the same.

Note #2: Any time you use a calculator to find a logarithm you will get a decimal approximation of the actual value. So these two answers, if you had a calculator with more decimal places may be different by a very, very small amount. (As you can see, the two answers we got here are the same to 16 decimal places.)