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What is the value of the logarithm below? (Round your answer to two decimal places.)

[tex]\(\log_4 12\)[/tex]

A. 1.08
B. 0.63
C. 1.79
D. 7.22

Sagot :

To determine the value of [tex]\( \log_4 12 \)[/tex], we need to find the exponent [tex]\( x \)[/tex] such that [tex]\( 4^x = 12 \)[/tex].

First, observe that [tex]\( \log_4 12 \)[/tex] can be transformed using the change of base formula:
[tex]\[ \log_4 12 = \frac{\log 12}{\log 4} \][/tex]

Here, [tex]\(\log\)[/tex] denotes the logarithm to the base 10, which is commonly available on calculators.

Next, let's compute this value:
[tex]\[ \log 12 \approx 1.08 \][/tex]
[tex]\[ \log 4 \approx 0.60 \][/tex]

Now, we divide these two values:
[tex]\[ \frac{1.08}{0.60} \approx 1.80 \][/tex]

After performing careful calculations, you will get the exact value. When rounded to two decimal places, the value of [tex]\( \log_4 12 \)[/tex] is:

[tex]\[ 1.79 \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{1.79} \][/tex]