Problem 84

Question

Evaluate or simplify each expression without using a calculator. $$\log 10^{8}$$

Step-by-Step Solution

Verified
Answer
The simplification of the expression \( \log 10^{8} \) renders 8.
1Step 1: Understanding the expression
The given expression is \( \log 10^{8} \). The base of the logarithm here is 10 (since there's no other number indicating the base, it's 10), and the argument of the logarithm is \(10^{8}\). The general rule for logs is that logb(b^a) = a.
2Step 2: Applying logarithmic property
By this general rule, we conclude that the expression \( \log 10^{8} = 8 \) because it follows the format of logb(b^a) = a, where b is the base 10, and a is the power 8 in this scenario.