To solve the equation \(2^x = 2048\), follow these steps:

1. **Express 2048 as a power of 2:**  
   We need to find an integer \(x\) such that \(2^x = 2048\). Start by determining if 2048 is a power of 2.

   \[
   2048 = 2^{11}
   \]

2. **Set the exponents equal to each other:**  
   Since \(2^x = 2^{11}\), the exponents must be equal. Therefore, 

   \[
   x = 11
   \]

So, the solution is \(x = 11\).

Would you like further details on how to find powers of 2 or do you have any other questions?

Here are 8 related questions that might interest you:

1. How can you solve \(3^x = 81\) using similar steps?
2. What is the general method for solving \(a^x = b\)?
3. How can you solve an equation like \(2^x = 50\) when 50 is not a power of 2?
4. What if the equation was \(2^{2x} = 2048\)? How would the solution change?
5. How do logarithms relate to solving exponential equations like this?
6. What are some common powers of 2 to memorize?
7. How would you solve \(5^x = 3125\)?
8. What if the equation was \(2^x = 0.5\)? How would you solve it?

**Tip:** Remember that recognizing common powers of numbers (like powers of 2, 3, or 5) can greatly speed up solving exponential equations.

Learn how to solve the equation 2^x = 2048 step-by-step with a detailed solution. Understand the concept of exponential functions and how to find powers of numbers efficiently. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation