Problem 1 - College Algebra Essentials

Question

Write each equation in its equivalent exponential form. $$4=\log _{2} 16$$

Step-by-Step Solution

Answer

The equivalent exponential form for the logarithmic equation \( 4 = \log _{2} 16 \) is \( 2^4 = 16 \).

Step 1: Identifying the Parts

The first step is to identify the different parts of the logarithmic equation: \( \log_b a = c \). In the exercise, \( b \) is 2, \( a \) is 16, and \( c \) is 4.

Step 2: Convert the Logarithmic Form to the Exponential Form

We will use the formula for converting logarithmic form to exponential form, which is \( b^c = a \) . In this case, \( b \) is 2, \( c \) is 4, and \( a \) is 16. Substituting the values, we get the exponential form as \( 2^4 = 16 \).

Step 3: Verify the Result

To verify the result, we find \( 2^4 \) equals 16, which means our conversion was correct.