Problem 66 - College Algebra

Question

Evaluate each expression without using a calculator. $$10^{\log 53}$$

Step-by-Step Solution

Answer

The value of the expression \(10^{\log 53}\) is 53.

Step 1: Recognize the property

Recognize the property of logs and exponentials that for any number b and x, \(b^{\log_{b}x} = x \). Here, the given expression, \(10^{\log10 53}\) has the same form.

Step 2: Applying the property

Apply the property to the given equation. Using this property, if we take base 10, and x equals 53, then \(10^{\log10 53} = 53\).