Gven
The lograthmic function, lograthmic fu
[tex]y=\log_4x[/tex]
To find:
a) Rewrite the function in exponential form.
b) For each given value of y, find the value of x to complete the ordered pair.
c) The graph of the function.
Explanation:
It is given that,
[tex]y=\log_4x[/tex]
a) Since,
It is known that,
[tex]\begin{gathered} y=\log_ax \\ \Rightarrow x=a^y \end{gathered}[/tex]
Then,
[tex]x=4^y[/tex]
Hence, the exponential form of the function is,
[tex]x=4^y[/tex]
b) Also,
For y = -2,.
The value of x is given by,
[tex]\begin{gathered} \\ \Rightarrow x=4^{-2} \\ \Rightarrow x=\frac{1}{4^2} \\ \Rightarrow x=\frac{1}{16} \end{gathered}[/tex]
Hence, the ordered pair is (1/16, -2).
For y = -1,
[tex]\begin{gathered} x=4^{-1} \\ x=\frac{1}{4} \end{gathered}[/tex]
Hence, the ordered pair is (1/4, -1).
For y = 0,
[tex]\begin{gathered} x=4^0 \\ x=1 \end{gathered}[/tex]
Hence, the ordered pair is (1, 0).
For y = 1,
[tex]\begin{gathered} x=4^1 \\ x=4 \end{gathered}[/tex]
Hence, the ordered pair is (4, 1).
For y = 2,
[tex]\begin{gathered} x=4^2 \\ x=16 \end{gathered}[/tex]
Hence, the ordered pair is (16, 2).
c) Also, the graph of the given function is,
