Problem 65 - College Algebra

Question

Evaluate each expression without using a calculator. $$10^{\log 33}$$

Step-by-Step Solution

Answer

The evaluation of the expression \(10^{\log 33}\) equals 33.

Step 1: Understand the properties of logarithms

Firstly, remember one of the key properties of logarithms: For any base \(b\) and any positive number \(x\), \(b^{(\log_{b}x)}=x\). Specifically, in this case, it will be used that \(10^{(\log10 x)}=x\).

Step 2: Apply the logarithmic property to the given expression

Now it's time to apply the property stated above: \(10^{\log 33} = 33\). According to the properties of logarithms, any base \(b\) raised to the logarithm base \(b\) of a number equals the number itself. Therefore, \(10^{(\log10 33)}=33\).