Final answer:
The expression log₁₀ √10 evaluates to 0.5 because the logarithm of a square root is one-half the logarithm of the number under the root, and log₁₀ (10) is 1.
Step-by-step explanation:
To evaluate the expression log₁₀ √10, we need to understand the relationship between logarithms and exponents. The expression can be rewritten using the property that the logarithm of a square root is equal to one-half the logarithm of the number under the root:
log₁₀ (√10) = log₁₀ (10^{1/2})
Since log₁₀ (10) = 1, because 10 to the first power is 10, we can simplify our expression further:
log₁₀ (10^{1/2}) = ½ × log₁₀ (10) = ½ × 1 = ½
Therefore, the evaluated expression is 0.5.