https://file.aiquickdraw.com/mathbot/file/172952849259889eqk4uk.jpg

The equation shown in the image is:

\[
4 \times (2.5)^{2x} = 4
\]

To solve for \( x \), follow these steps:

### Step 1: Divide both sides by 4
\[
(2.5)^{2x} = 1
\]

### Step 2: Recognize that any number raised to the power of 0 equals 1
\[
(2.5)^{2x} = (2.5)^0
\]

### Step 3: Set the exponents equal to each other
Since the bases are the same, we can set the exponents equal:
\[
2x = 0
\]

### Step 4: Solve for \( x \)
\[
x = 0
\]

Thus, the value of \( x \) is \( 0 \).

Would you like further details or explanations on any part of this process?

Here are five related questions to explore:

1. What happens when the base of an exponential equation is less than 1?
2. How can we solve exponential equations with different bases?
3. What is the logarithmic form of an exponential equation?
4. How would the solution change if the base was negative?
5. What if the exponent was a fractional number?

**Tip:** Always simplify the equation first by isolating the exponential term before applying logarithmic or algebraic methods.

What value of x satisfies this equation? 4(2.5)^(2x) = 4

Learn how to solve the exponential equation 4(2.5)^(2x) = 4 with a step-by-step solution. This problem explores properties of exponents and algebraic simplification. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation