SOLUTION: Graphs this following function. g(x)=-log(1/2)(x-1)

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Question 382397: Graphs this following function.
g(x)=-log(1/2)(x-1)

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
To graph this we need a table of values. For a table of values you pick values for x and use the function to find the function's value for that x. Each pair of numbers represents a point on the graph. Plot these points. Keep finding and plotting points until you get an idea of what kind of curve is being formed. Then sketch in the rest of the curve.

There are a couple of ways to build this table of values:
  • Clever: Pick x values such that x-1 is a power of 1/2. These logarithms can be found "by hand". For example, if x = 3 then x-1 is 2 and since 2+=+%281%2F2%29%5E%28-1%29 the base 1/2 logarithm of 2 would be -1. This gives us a point: (3, -1). Another example would be x = 2 making x-1 a 1. And since 1+=+2%5E0 the logarithm will be 0. Our point: (2, 0).
  • Convert the base 1/2 logarithm to an expression of base 10 (or base e) logarithms so we can use our calculators. This conversion is done using the base conversion formula for logarithms:
    log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29
    Using this formula to convert your logarithm we get:
    g%28x%29+=+log%28%281%2F2%29%2C+%28x-1%29%29+=+log%28%28x-1%29%29%2Flog%28%281%2F2%29%29
    Since log(1/2) = -0.3010299956639812 this becomes:
    g%28x%29+=+log%28%281%2F2%29%2C+%28x-1%29%29+=+log%28%28x-1%29%29%2F-0.3010299956639812
    (You probably want to round off that long decimal.) Now you can pick any number you want for x (as long as it is greater than 1). Then you can use your calculator to find the function's value for each x.