Problem 24 - College Algebra Essentials

Question

Evaluate each expression without using a calculator. $$\log _{3} 27$$

Step-by-Step Solution

Answer

3

Step 1: Identify the Logarithmic Base and Result

The statement \(\log _{3} 27\) can be seen as follows: what power should 3 be raised to, in order to get 27? Putting it another way, this is the same as asking: \(3^x = 27\). The logarithmic base is 3 and the result is 27.

Step 2: Identify the response

We need to know the power we can raise 3 to, which will give 27. Here, the power is the \(x\) in the equation from step 1. The power in our case is 3 since \(3^3 = 27\). Therefore, \(x = 3\).

Step 3: Final Answer

To evaluate the expression \(\log _{3} 27\), the answer is the power to which 3 must be raised to get 27, which is 3.