To find the value of \(\log_{2} 43\) using the change of base formula, we can use the formula:
\[ \log_{b} a = \frac{\log_{c} a}{\log_{c} b} \]
We can use base 10 (or natural logarithm, base e) for our calculations. For this example, we'll use base 10.
Using the change of base formula:
\[ \log_{2} 43 = \frac{\log_{10} 43}{\log_{10} 2} \]
Now, we can calculate \(\log_{10} 43\) and \(\log_{10} 2\) using a calculator:
\[ \log_{10} 43 \approx 1.633 \] \[ \log_{10} 2 \approx 0.301 \]
Substituting these values into the change of base formula gives:
\[ \log_{2} 43 \approx \frac{1.633}{0.301} \approx 5.426 \]
Rounding to the nearest thousandth, we find:
\[ \log_{2} 43 \approx 5.426 \]
Thus, the value equivalent to \(\log_{2} 43\) rounded to the nearest thousandth is 5.426.
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