Problem 2 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The equivalent exponential form of the given logarithm equation will be \(2^6 = 64\).

Step 1: Identify the components of logarithmic equation

In the given logarithmic equation, \(6=\log _{2} 64\), 2 is the base of logarithm, 64 is the argument and 6 is the value of this logarithm. Logarithm equations can be converted into equivalent exponential equations using the rule that \(\log _{b} a = c\) is equivalent to \(b^c = a\)

Step 2: Convert to exponential form

Following the rule \(\log _{b} a = c\) is equivalent to \(b^c = a\), the given logarithm can be converted to exponential form: \(2^6 = 64\).