SOLUTION: How to put Log2(x-3)+1 in the calculator and how to get the domain and range? please

Question 573985: How to put Log2(x-3)+1 in the calculator and how to get the domain and range? please
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

I've never seen or heard of a calculator that can do base 2 logarithms. They usually only do base 10 and/or base e (aka ln) logarithms. So is you need to calculate base 2 logarithms, you will need to use the base conversion formula:

to convert your base 2 log into either base 10 or base e logarithms:

Now you can use your calculator with either one of the expressions on the right.

To find the domain and range of your expression you do not need to do the above. For the domain, you just have to restrict the domain to only those values of x that make the argument of the logarithm positive. So to find the domain just that the argument, x-3, set it equal to zero and solve it:
x - 3 > 0
Adding 3 to each side we get:
x > 3
This is the domain for you expression.

For the range we just need to do a little thinking. Your expression is the sum of a logarithm and 1. Since logarithms are exponents and exponents can be any number, the logarithm in your expression can turn out to be any real number. And if you add 1 to any real number, you will get any real number as a result. So the range for your expression is all Real numbers.

If you doubt either the domain or range, then enter either of the following equations into a graphing calculator:

and look at the graph. You will see that no part of the graph is on or to the left of the vertical line x = 3 (illustrating the domain) yet every horizontal line, y = a, will hit the graph somewhere (illustrating that the y can be any number).
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