1. The problem is to find the value of $\log_2(20)$.\n\n2. Recall the definition of logarithm: $\log_b(a)$ is the exponent to which the base $b$ must be raised to get $a$.\n\n3. We want to find $x$ such that $2^x = 20$.\n\n4. Since 20 is not a power of 2, we use the change of base formula: $$\log_2(20) = \frac{\log_{10}(20)}{\log_{10}(2)}.$$\n\n5. Using approximate values: $\log_{10}(20) \approx 1.3010$ and $\log_{10}(2) \approx 0.3010$.\n\n6. Substitute these values: $$\log_2(20) \approx \frac{1.3010}{0.3010}.$$\n\n7. Simplify the fraction: $$\log_2(20) \approx 4.32.$$\n\nTherefore, the value of $\log_2(20)$ is approximately 4.32.