Problem 22 - College Algebra

Question

Evaluate each expression without using a calculator. $$\log _{7} 49$$

Step-by-Step Solution

Answer

The value of \(\log_{7}{49}\) is 2.

Step 1: Understand the logarithmic notation

A logarithm \(\log_{b}{a}\) is the exponent to which we must raise the base \(b\) to get the number \(a\). So if you have \(\log_{b}{a}=x\), then you should think of it as \(b^x=a\). You can apply this concept to our problem \(\log_{7}{49}\). The problem is actually asking what power you have to raise 7 (the base) in order to get 49.

Step 2: Apply the power of base to the logarithmic expression

In this case, you need to think about what power to raise 7 in order to get 49. In this instance, you'll realize that if you square 7 (i.e., \(7^2=49\)), you get 49. Hence, the power is 2.

Step 3: Write the final result

So, according to the calculation and the notation of the logarithm, \(\log_{7}{49}\) equals 2.