Let's solve the equation \( 4^{2x} + 3 = 1 \).

### Step 1: Isolate the exponential term.
\[
4^{2x} = 1 - 3
\]
\[
4^{2x} = -2
\]

### Step 2: Analyze the equation.
The equation \( 4^{2x} = -2 \) does not have a solution because exponential functions (like \( 4^{2x} \)) always yield positive results. In other words, no real value of \( x \) will make \( 4^{2x} = -2 \).

Thus, there is **no real solution** to the equation.

Would you like any further details or clarifications?

Here are 5 questions related to this:
1. How do exponential functions behave for different bases?
2. What is the general process for solving exponential equations?
3. Can exponential equations ever have negative results?
4. What is the significance of the base in exponential functions?
5. How would this equation change if the right-hand side was positive?

**Tip**: Always check if an exponential equation yields a positive result, as exponents with real numbers can't result in a negative value.

Learn how to solve the exponential equation 4^2x + 3 = 1. This problem focuses on the behavior of exponential functions and explores why exponential equations with real numbers cannot result in negative values. 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