Problem 9 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: Understanding the terms in the equation

In the exponential form \(a^{b}=c\), 'a' is the base, 'b' is the exponent and 'c' is the result.

Step 2: Writing the equivalent logarithmic form

Now to write the equivalent logarithmic form we use the rules of logarithms. The exponential equation \(a^{b}=c\) can be rewritten in logarithmic form as \( \log_{a}c = b\), which means log of 'c' to the base 'a' equals 'b'.

Step 3: Substituting the values

In our equation \(2^{3}=8\), 2 is the base (a), 3 is the exponent (b) and 8 is the result (c). Substituting these into logarithmic form, we have \( \log_{2}8 = 3\).