Final answer:
The answer is -4. Therefore, the evaluation of \(-\log(0.0001)\) gives us the answer of \(4\), which corresponds to the choice (b) 4.
Step-by-step explanation:
To evaluate -log(0.0001), we can rewrite it as log(0.0001) with a negative sign in front. Logarithm is the inverse operation of exponentiation, so log(0.0001) represents the power that 10 needs to be raised to in order to get 0.0001. In this case, log(0.0001) = -4, so the answer is option a) -4.
To evaluate \(-\log(0.0001)\), we first need to understand what a logarithm is. A logarithm with base 10 (commonly denoted as \(\log\) with no base specified) is the exponent to which 10 must be raised to get a certain number. Here's how you can do this step-by-step:
Step 1: Identify the number we will take the logarithm of. In this case, it's 0.0001.
Step 2: Remember that when no base is indicated, the common logarithm (base 10) is assumed. Thus, we are trying to find out the power to which 10 must be raised to yield 0.0001. We can express this as: \[10^x = 0.0001\]
Step 3: Convert the number 0.0001 into a power of 10 to make it easier to identify x: \[0.0001 = 10^{-4}\] This is because \(\frac{1}{10000} = \frac{1}{10^4} = 10^{-4}\).
Step 4: Since we have expressed 0.0001 as \(10^{-4}\), we know that: \[\log(0.0001) = \log(10^{-4}) = -4\] Step 5: We are evaluating \(-\log(0.0001)\), which is the negation of the result from
Step 5: \[-\log(0.0001) = -(-4) = 4\] Therefore, the evaluation of \(-\log(0.0001)\) gives us the answer of \(4\), which corresponds to the choice (b) 4.