Question - Evaluating Logarithmic Expressions
Solution:
To solve this problem, let's evaluate each logarithmic expression and see if it has been evaluated correctly.A. ln(0) = 1This is incorrect because the natural logarithm of zero is undefined. ln(0) does not have a real value since you cannot raise e (Euler's number, approximately 2.71828) to any power to get zero.B. log₂(8) = 3This is correct because 2 raised to the power 3 equals 8. (2^3 = 8)C. log(0.1) = -1This is correct because 10 raised to the power -1 equals 0.1. (10^-1 = 0.1)D. log₂(-1) = 0.5This is incorrect because you cannot take the logarithm of a negative number in the real number system. log₂(-1) is undefined.E. log(0.025) = -2This is incorrect because 10 raised to the power of -2 equals 0.01, not 0.025. We need to find the actual value of log(0.025) to see if it equals -2.Let's calculate the actual value of log(0.025), which means we are looking for the exponent that 10 must be raised to in order to get 0.025.Using a calculator, log(0.025) ≈ -1.60206 Therefore, the options B and C have been evaluated correctly.
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