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]
