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Is there anyone that can assist me with this problem?

Is there anyone that can assist me with this problem?-example-1
User Dodjs
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1 Answer

3 votes

Answer:

The correct answer is option b) 81

Step-by-step explanation:

The definition of log is:


\log_ab=c\Leftrightarrow a^c=b

In this case, we are given:


y=\log_cx

And we know that the point (x, y) = (27, 3) lies on the graph of the given function.

We can write:


3=\log_c27

Applying the log definition:


3=\operatorname{\log}_c27\Leftrightarrow c^3=27

Now we can solve for c:


\begin{gathered} c^3=27 \\ c=\sqrt[3]{27}=3 \end{gathered}

Since c = 3, now we can find the value of k.

We are given:


y=c^x

And (x, y) = (4, k) lies in the graph.

Then:


k=3^4=81

Thus, k = 81

User Canesin
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