Question 171900: We are trying to help my friends son start to solve the following equation prior to graphing: f(x)=log3(x-1). How do you set the problem up to solve? Perhaps the first 3 steps would help us remember since it has been 30 years since we took college algebra. Not in book.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! We are trying to help my friends son start to solve the following equation prior to graphing: f(x)=log3(x-1). How do you set the problem up to solve? Perhaps the first 3 steps would help us remember since it has been 30 years since we took college algebra. Not in book.
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f(x)=log3(x-1)
Usually, y is substituted for f(x) to graph equations.
You can graph this by picking values for x, then solving for y and plotting the points (x,y). It will give a logarithmic curve.
Logs base 3 aren't common. Calculators have logs base 10, usually labelled Log, and "natural logs", labelled ln.
To find logs base 3, divide the log base 10 by the log of 3. For example, at x = 5,  .
While this complicates the calculations, the plots of logs to any base look the same, just compressed or expanded.
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This equation gives a line of infinite length, and any point on it is a solution to the equation. There is no single, or unique, solution to it. All values of x greater than 1 will give a corresponding value of y, or f(x). Logs of numbers less than or = zero are not defined.
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Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! We are trying to help my friends son start to solve the following equation prior to graphing: f(x)=log3(x-1). How do you set the problem up to solve? Perhaps the first 3 steps would help us.
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I'm going to assume that "3" is the base of the logarithm. If that is
correct you have the following:
y = log3 (x-1)= [log(x-1)]/[log3] = [log(x-1)]/0.4771
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Comment: Your friend's son may recognize that the line x=1 is a vertical
asymptote for the graph.
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Now plot three points:
Let x = 2, then y=[log(1)]/0.4771 = 0/0.4771 = 0; gives you point(2,0)
Let x = 4, then y=[log(3)]/0.4771 = =1 ; gives you point (4,1)
Let x = 10, then y = [log(9)/0.4771] = 2 ; gives you point (10,2)
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Plot these points and keep in mind that x=1 is a vertical asymptote
and you have all the information you need to graph the function.
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Cheers,
stan H.
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