Question

no calculator is allowed on this question.
which logarithmic function models the graph shown above?
select one answer
a ( f(x) = \frac{1}{5}log x )
b ( f(x) = log_{5} x )
c ( f(x) = 5log x )
d ( f(x) = \frac{1}{4}log_{5} x )
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Explanation:

Step1: Identify the point on the graph

The graph passes through \((5, 1)\) and \((1, 0)\). Let's test each function with \(x = 5\) and \(x = 1\).

Step2: Test Option B: \(f(x)=\log_{5}x\)

For \(x = 1\): \(\log_{5}1 = 0\) (since \(\log_{a}1 = 0\) for any \(a>0,a
eq1\)), which matches the point \((1, 0)\).
For \(x = 5\): \(\log_{5}5 = 1\) (since \(\log_{a}a = 1\) for any \(a>0,a
eq1\)), which matches the point \((5, 1)\).

Let's check other options to confirm:

• Option A: \(f(5)=\frac{1}{5}\log 5

eq1\) (base 10 log, \(\log 5\approx0.699\), \(\frac{1}{5}\times0.699\approx0.14
eq1\)).

• Option C: \(f(5)=5\log 5\approx5\times0.699\approx3.495

eq1\).

• Option D: \(f(5)=\frac{1}{4}\log_{5}5=\frac{1}{4}\times1 = 0.25

eq1\).

Answer:

B. \( f(x) = \log_{5} x \)