Math Problem Statement

3^x = 9. Solve for x.

Solution

The equation in the image is:

3x=93^x = 9

To solve for xx, let's express both sides in terms of the same base, if possible.

Solution:

  1. Notice that 9 can be written as a power of 3: 9=329 = 3^2

  2. Substitute 99 with 323^2: 3x=323^x = 3^2

  3. Since the bases are the same, we can set the exponents equal to each other: x=2x = 2

Answer:

x=2x = 2

Would you like more details on exponential equations or have any specific questions?

Here are five related questions to explore further:

  1. How do you solve exponential equations when the bases are different?
  2. What happens if the exponent is a fraction?
  3. Can you solve 2x=162^x = 16 using a similar approach?
  4. What are some real-world applications of exponential equations?
  5. How do logarithms help in solving exponential equations?

Tip: When solving exponential equations, try to express both sides with the same base to simplify the solution process.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Exponential Equations

Formulas

a^x = a^y implies x = y if a > 0 and a ≠ 1

Theorems

Exponent Properties

Suitable Grade Level

Grades 8-10