I can graph and apply logarithmic functions. Logarithmic functions are inverses of exponential functions. Review Let f(x) = 2x + 1. Sketch a graph. Does.

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Presentation transcript:

I can graph and apply logarithmic functions

Logarithmic functions are inverses of exponential functions. Review Let f(x) = 2x + 1. Sketch a graph. Does this function have an inverse? Why or why not? How would you graph the inverse? How would you find the equation of the inverse? Can you see how these two equations “undo” each other?

Let f(x) = b x. (Assume b>1 ) Does this function have an inverse? So if y = b x, then the inverse is x=b y. Graph both functions. Compare the domains, ranges, asymptotes, and intercepts for the two graphs. But how do we solve for y in this second function? We define y = log b x. (The function y is the exponent b is raised to produce x.)

So y = log b x means b y =x. Rewrite in log form =8 2.e 0 = = 1/25 log x means log 10 x (common log) ln x means log e x (natural log)

Simplify 1.a) log 2 16 b) log 2 1/8 c) log 2 ( 3 √2) d) log 2 (-8) 2.a) log 8 8b)log c)log a) log 100b)log.1 4.a) ln eb)ln e 3 c)ln (1/e)

6.log a) b) c)

Problems 1.Compare log 3 10 and log Graph y = log 2 x and y = -log 2 x. Does y = log 2 x have a horizontal asymptote? When does it reach a value of 10? 3.Find the domain of log 2 (12-4x). 4.Graph y = ln x and y = ln(x -1). 5.Solve. a)310 2x = 6b)e 3t-1 + 5= 7

Common Mistakes 1.Simplify log 2 8 log Simplifylog Be very careful!