Answer:
[tex]x \to f(x)[/tex]
[tex]0.25 \to -1[/tex]
[tex]0.5 \to -0.5[/tex]
[tex]1 \to 0[/tex]
[tex]2 \to 0.5[/tex]
[tex]4 \to 1[/tex]
[tex]8 \to 1.5[/tex]
Step-by-step explanation:
Given
[tex]f(x) = log_4(x)[/tex]
[tex]x = 0.5[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(0.5) = log_4(0.5)[/tex]
Apply law of logarithm
[tex]f(0.5) = \frac{log(0.5)}{log(4)}[/tex]
Using a calculator, we have:
[tex]f(0.5) = -0.5[/tex]
[tex]x = 1[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(1) = log_4(1)[/tex]
Express 1 as 4^0
[tex]f(1) = log_4(4^0)[/tex]
Apply law of logarithm
[tex]f(1) = 0*log_4(4)[/tex]
[tex]f(1) = 0[/tex]
[tex]x = 2[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(2) = log_4(2)[/tex]
Apply law of logarithm
[tex]f(2) = \frac{log(2)}{log(4)}[/tex]
Using a calculator, we have:
[tex]f(2) = 0.5[/tex]
[tex]x = 4[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(4) = log_4(4)[/tex]
[tex]log_a(a) = 1[/tex]
So:
[tex]f(4) = 1[/tex]
[tex]x = 8[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(8) = log_4(8)[/tex]
Apply law of logarithm
[tex]f(8) = \frac{log(8)}{log(4)}[/tex]
Using a calculator, we have:
[tex]f(8) = 1.5[/tex]
So, the complete table is:
[tex]x \to f(x)[/tex]
[tex]0.25 \to -1[/tex]
[tex]0.5 \to -0.5[/tex]
[tex]1 \to 0[/tex]
[tex]2 \to 0.5[/tex]
[tex]4 \to 1[/tex]
[tex]8 \to 1.5[/tex]
