Question

Is there anyone that can assist me with this problem?

Answer 1

Answer:

The correct answer is option b) 81

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