https://file.aiquickdraw.com/mathbot/file/1725717657821jqqx6utz.jpg

The given equation is:

\[
2^x \cdot 3^{x+2} = 324
\]

We need to solve for \( x \). Let's break this down step by step:

1. Rewrite the equation in a simpler form:
   \[
   2^x \cdot 3^{x+2} = 324
   \]

   This can be expanded as:
   \[
   2^x \cdot 3^{x} \cdot 3^2 = 324
   \]
   Since \( 3^2 = 9 \), the equation becomes:
   \[
   2^x \cdot 3^x \cdot 9 = 324
   \]

2. Divide both sides by 9:
   \[
   2^x \cdot 3^x = \frac{324}{9} = 36
   \]

3. The left-hand side can be written as:
   \[
   (2 \cdot 3)^x = 36
   \]
   Simplifying \( 2 \cdot 3 = 6 \), the equation becomes:
   \[
   6^x = 36
   \]

4. Since \( 36 = 6^2 \), we can write:
   \[
   6^x = 6^2
   \]

5. Equating the exponents:
   \[
   x = 2
   \]

Thus, the solution is \( x = 2 \), which corresponds to option A.

Would you like further details on any of the steps or have any questions?

Here are 5 related questions to explore this concept further:
1. How would you solve \( 2^x \cdot 3^{x+3} = 972 \)?
2. Can you solve the equation \( 5^x \cdot 4^{x+1} = 500 \)?
3. How can logarithms be used to solve \( 2^x \cdot 5^x = 

Nilai x yang merupakan penyelesaian dari persamaan 2^x . 3^(x+2) = 324 adalah ...

Learn how to solve the exponential equation 2^x * 3^(x+2) = 324 with a detailed step-by-step solution. This problem explores exponent rules and algebraic manipulation. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation