We are tasked with solving the equation:

\[
2^x \cdot 5 = 10^x
\]

### Step 1: Rewrite \(10^x\) using its prime factors
We know that \(10^x = (2 \cdot 5)^x = 2^x \cdot 5^x\). So, we can rewrite the equation as:

\[
2^x \cdot 5 = 2^x \cdot 5^x
\]

### Step 2: Simplify the equation
Now, divide both sides of the equation by \(2^x\) (assuming \(x \neq 0\)):

\[
5 = 5^x
\]

### Step 3: Solve for \(x\)
We can observe that the equation \(5 = 5^x\) holds true when \(x = 1\).

Thus, the solution to the equation is:

\[
x = 1
\]

Would you like more details on any part of the solution? Here are five related questions for further practice:

1. Solve \(2^{x+1} \cdot 3 = 6^x\).
2. Find the solution to \(3^x \cdot 4 = 12^x\).
3. Solve \(2^x \cdot 3 = 18^x\).
4. Solve the equation \(7^x \cdot 2 = 14^x\).
5. Solve for \(x\) in the equation \(9^x \cdot 2 = 18^x\).

**Tip:** When solving exponential equations, try rewriting the terms with the same base to simplify.

Discover the step-by-step solution to the equation 2^x * 5 = 10^x using prime factorization and properties of exponents. This problem is designed for students in Grades 8-10 and helps build algebraic skills for solving exponential equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation