what is the value of log₄16?\n1\n2\n4\n8

Explanation:

Step1: Recall log - definition

Let $y = \log_{4}16$. By the definition of logarithms, if $y=\log_{a}x$, then $a^{y}=x$. So, if $y = \log_{4}16$, then $4^{y}=16$.

Step2: Rewrite 16 in terms of 4

We know that $16 = 4\times4=4^{2}$. So the equation $4^{y}=16$ becomes $4^{y}=4^{2}$.

Step3: Equate the exponents

Since the bases are the same ($a^{m}=a^{n}$ implies $m = n$ for $a>0,a\neq1$), when $4^{y}=4^{2}$, we have $y = 2$.

Answer:

B. 2