Problem 35 - College Algebra

Question

Evaluate each expression without using a calculator. $$\log _{5} 5^{7}$$

Step-by-Step Solution

Answer

The result of the expression \(\log _{5} 5^{7}\) is 7.

Step 1: Apply Logarithm Rule

One of the rules of logarithms states that for any base \(b\), \(\log _{b} b^{x} = x\). Here in the exercise, \(b = 5\) and \(x = 7\). So we can directly apply this rule.

Step 2: Calculate Result

After applying the logarithm rule, the equation \(\log _{5} 5^{7}\) simplifies to 7. So, the result of \(\log _{5} 5^{7}\) is 7.