Question

the function f is logarithmic, and the points (2,1) and (4,2) are on the graph of f in the xy - plane. which of the following could define f(x)?
a ( log_{4}x )
b ( 2log_{2}x )
c ( 2log_{4}x )
d ( log_{4}(x + 2) )

Explanation:

Step1: Test point (2,1) for option C

Substitute $x=2$ into $2\log_{4}2$: $2\times\frac{1}{2}=1$, matches.

Step2: Test point (4,2) for option C

Substitute $x=4$ into $2\log_{4}4$: $2\times1=2$, matches.

Step3: Verify other options

Option A: $\log_4 2=\frac{1}{2}
eq1$; Option B: $2\log_2 2=2
eq1$; Option D: $\log_4(2+2)=1$, but $\log_4(4+2)
eq2$. Only C works.

Answer:

C. $2\log_{4}x$