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Use f(x) = log5 (x) as the parent function. For the following exercises, write a logarithmic equation corresponding...

For the following exercises, write a logarithmic equation corresponding to the graph shown.

Use f(x) = log5 (x) as the parent function.

Expert Solution

Refer to the graph shown in the textbook. From the graph the vertical asymptote is x = 5 and has been vertically reflected. Thus the equation will be in the form;

y = blog5(-x + 5) + k

It appears the graph passes through the points (0, 2) and (4, 0) substitute (4, 0) as follows:

0 = alog5(-4 + 5) + k

0 = alog5(1) + k

0 = 0 + k

k = 0

Now substitute (0, 2) as follows:

2 = alog5(-0 + 5) + 0

2 = alog5(5)

a = 2

Thus the equation of the function is y = 2log5(-x + 5).

Now check the equation by graphing the function as shown below:

Thus the equation of the function is y = 2log5(-x + 5).

Junaid answered 1 year ago

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