Problem 63 - College Algebra

Question

Evaluate each expression without using a calculator. $$\log 10^{7}$$

Step-by-Step Solution

Answer

7

Step 1: Identify the Base and the Exponent

Here, 10 is the base and 7 is the exponent. The expression can be written as \( \log 10^{7} \).

Step 2: Apply the Logarithm Property

Apply the logarithm property that states \( \log{b^x} = x \log{b} \). Thus, the given expression becomes \( 7 \log{10} \).

Step 3: Simplify the Expression

Since the base of the logarithm and the number are identical, \( \log{10} = 1 \). Therefore, our expression simplifies to \( 7 \times 1 = 7 \).