Problem 13 - College Algebra

Question

Write each equation in its equivalent logarithmic form. $$\sqrt[3]{8}=2$$

Step-by-Step Solution

Answer

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

Step 1: Identify the base and the exponent

In the given equation \( \sqrt[3]{8} = 2 \), 8 can be rewritten as \( 2^3 \), thus our base (b) is 2 and the exponent (y) is 3.

Step 2: Write in exponential form

Using the identified base and exponent, we rewrite the equation in its exponential form: \( 2^3 = 8 \).

Step 3: Convert to logarithmic form

Applying the rule \( b^y = x \) is equivalent to \( \log_b{x} = y \), we convert the equation into its logarithmic form: \( \log_2{8} = 3 \).