Evaluating the Expression: 2 + 1/2 log (10^(-3))
In this article, we will evaluate the expression 2 + 1/2 log (10^(-3)). To do this, we need to follow the order of operations (PEMDAS) and use the properties of logarithms.
Step 1: Evaluate the Logarithm
The logarithm in the expression is log (10^(-3)). Since the base of the logarithm is 10, we can rewrite it as:
log (10^(-3)) = -3 log (10)
Using the property of logarithms that states log (a) = 1, we can simplify the expression to:
log (10^(-3)) = -3
Step 2: Multiply by 1/2
Now, we need to multiply the result by 1/2:
1/2 (-3) = -3/2
Step 3: Add 2
Finally, we add 2 to the result:
2 + (-3/2)
To add these two numbers, we need to find a common denominator, which is 2. So, we can rewrite the expression as:
2 + (-3/2) = (4/2) + (-3/2) = (4 - 3)/2 = 1/2
Final Answer
Therefore, the final answer is:
2 + 1/2 log (10^(-3)) = 1/2
