Problem 9 - College Algebra

Question

Write each equation in its equivalent logarithmic form. $$2^{3}=8$$

Step-by-Step Solution

Answer

The equivalent logarithmic form of the equation \(2^{3}=8\) is \(log_2(8) = 3\).

Step 1: Identify elements in the given equation

In the given equation \(2^{3}=8\), \(2\) is the base, \(3\) is the exponent and \(8\) is the result of the exponentiation of the base.

Step 2: Apply the logarithm rules

We will now apply the rule of logarithms that states: if \(a = b^n\), then the logarithmic form of this expression is \(log_b(a) = n\). Plugging the values from the first step into the logarithmic form we get: \(log_2(8) = 3\).