https://file.aiquickdraw.com/mathbot/file/1727018327740k0ef5dk5.jpg

The equation presented is \( \log_w{32} = 5 \), and we need to solve for \( w \), given that \( w > 0 \).

### Steps to solve:

1. The equation is in logarithmic form, and we can convert it to exponential form. The general logarithmic equation \( \log_b{x} = y \) can be rewritten as:
   \[
   b^y = x
   \]
   In this case:
   \[
   w^5 = 32
   \]

2. To solve for \( w \), take the 5th root of both sides:
   \[
   w = \sqrt[5]{32}
   \]

3. Since \( 32 = 2^5 \), we have:
   \[
   w = \sqrt[5]{2^5} = 2
   \]

Thus, the value of \( w \) is \( \boxed{2} \).

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you convert a logarithmic equation to its exponential form?
2. What is the significance of the base in logarithmic functions?
3. Can you explain why \( \log_b{x} = y \) is equivalent to \( b^y = x \)?
4. What are some methods for simplifying logarithmic equations with different bases?
5. How do you solve exponential equations that are not perfect powers?

**Tip:** Always check if the base of a logarithm and the result are related by powers to simplify the equation quickly.

Solve for w in the equation log_w 32 = 5.

Learn how to solve for w in the equation log_w 32 = 5. This problem demonstrates converting logarithmic equations to exponential form, using key logarithmic concepts. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation