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What is the value of [tex]$\log _4 16$[/tex]?

A. 1
B. 2
C. 4
D. 8

Sagot :

GinnyAnswer
To determine the value of \(\log_4 16\), we need to figure out to what power we must raise 4 to get 16.

We begin by setting up the expression:

[tex]\[ \log_4 16 = x \][/tex]

This can be rewritten in exponential form as:

[tex]\[ 4^x = 16 \][/tex]

Next, we need to recall that 16 is a power of 4. Specifically, we can express 16 as:

[tex]\[ 16 = 4^2 \][/tex]

So, we substitute this back into our equation:

[tex]\[ 4^x = 4^2 \][/tex]

Since the bases are the same, we can equate the exponents:

[tex]\[ x = 2 \][/tex]

Thus, the value of [tex]\(\log_4 16\)[/tex] is [tex]\(\boxed{2}\)[/tex].
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