Use this page with Slide 4: Exploring Logarithmic Functions of Fitting Wealth-v-Health and Exploring Logarithmic Models (Desmos).

  • The blue curve is the graph of h(x) = 1 log2 x + 0. Its constants will remain set at a = 1, b = 2, and k = 0.

  • You can modify the red curve g(x) (which is hiding behind h(x)!) by changing its coefficients: a, b, and k.

Base b

Keep k at 0 and a at 1. Change the value of b as indicated on each grid below.

1 Sketch each graph and label the coordinates where x = 1, y = 1, y = 2 and y = 3.

b = 3

b = 5

b = 10

2 How does the value of b impact the shape of a logarithmic function?

3 What connections can you draw between the value of b and exponents?

Vertical Shift k

Set a to 1 and b to 2. Change the value of k as indicated on each grid below.

4 Sketch each graph and label the coordinate where x = 1.

k = - 10

k = 0

k = 10

5 How does the value of k impact the shape of a logarithmic function?

6 Why does y = k when x = 1?

Logarithmic Coefficient a

Set k to 0 and b to 10, then zoom out out so you can see as far as x = 1,000.

Change h(x) to h(x) = 1 log10 (x) + 0 so that the blue curve lands on top of the red curve.

7 In each graph, label the coordinates where x = 10 and x = 100 and x = 1000.

a = - 2

a = 0

a = 2

8 What is the value of x when 1log2(x) = 4? What about when 2 log4(x) = 4? When 3 log8(x) = 4?

★ How are a and b related?

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