Problem 64 - College Algebra

Question

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

Step-by-Step Solution

Answer

8

Step 1: Identify the elements within the logarithmic expression

The base of the logarithm is 10 and the number inside the logarithm (this is the expression we want to find the power for to obtain 10) is \(10^{8}\).

Step 2: Apply the property of logarithms

The property of logarithms states that the log base b of b to the power of any number n, \(\log_{b}{b^{n}}\), equals n. Apply this property to the given logarithmic expression, \(\log{10^{8}}\).

Step 3: Calculate the final result

Applying the property, the answer to the logarithmic expression \(\log_{10}{10^{8}}\) is 8.