SOLUTION: Logarithms using change of base formula; log2(19) The 2 is very small and on the bottom and the 19 is large. Can you help me to understand how to do this problem? Thanks Debbie

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Question 419359: Logarithms using change of base formula;
log2(19)
The 2 is very small and on the bottom and the 19 is large.
Can you help me to understand how to do this problem? Thanks
Debbie
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
If you're talking about

then this is called "the base 2 logarithm of 19". It represents the exponent you would put on a 2 to get a 19:

I think your problem is to find out what number is this exponent you put on a 2 to get 19.

Some logarithms are easy to find. For example is the exponent for 5 that results in 25. We know what exponent on a 5 results in 25. It is 2. So .

But what exponent on a 2 results in 19? and so the exponent that results in 18 is going to be somewhere between 4 and 5. This is about as far as we can reasonably go without the help of a calculator.

But how do we use a calculator to find ? There is no button for base 2 logarithms. The base of a logarithm can be any positive number (except 1). So it would seem calculators would need an infinite number of buttons to handle all the different possible logarithms.. Instead of having a button for each logarithm your calculator your calculator has buttons for logarithms of just one or two bases, 10 and/or "e". The base 10 log button has "log" on it and the base e log button has "ln" on it. To find logarithms of other bases you use the change of base formula:

Or we could use base e logarithms:

Both of these will work and they will both result in the same answer. Just use your calculator to find the two logarithms and then divide them.