Problem 2 - College Algebra

Question

Write each equation in its equivalent exponential form. $$6=\log _{2} 64$$

Step-by-Step Solution

Answer

The exponential form of the equation is \(2^6 = 64\).

Step 1: Identify the base, exponent and result

In the given equation \(6 = \log _{2} 64\), base is 2, the result is 64 and the exponent is 6.

Step 2: Convert into exponential form

Following the relationship \(b^n = a\), the base becomes the base in the exponential equation, the expression on the other side of the equation becomes the exponent and the result is the value the base raised to the power equals. Therefore, the equation in exponential form is \(2^6 = 64\).