To find the value of \(\log_{2} 43\) using the change of base formula, we can convert it to logarithms with base 10 or base \(e\). The change of base formula states that:
\[ \log_{b} a = \frac{\log_{c} a}{\log_{c} b} \]
We can use base 10 (common logarithm):
\[ \log_{2} 43 = \frac{\log_{10} 43}{\log_{10} 2} \]
Now we need to calculate \(\log_{10} 43\) and \(\log_{10} 2\).
Using a calculator, we get:
\(\log_{10} 43 \approx 1.6335\)
\(\log_{10} 2 \approx 0.3010\)
Now, we can substitute these values into the formula:
\[ \log_{2} 43 \approx \frac{1.6335}{0.3010} \]
Calculating this gives:
\[ \log_{2} 43 \approx 5.426 \]
Thus, the value of \(\log_{2} 43\) to the nearest thousandth is approximately \(5.426\).
The equivalent value is:
3) 5.426
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