https://file.aiquickdraw.com/mathbot/file/1725622373268e2l5yv6w.jpg

The equation in the image is:

\[
\frac{1}{81} = 3^x
\]

We need to solve for \(x\).

### Solution:
First, express \( \frac{1}{81} \) as a power of 3.

Since \( 81 = 3^4 \), we have:
\[
\frac{1}{81} = 3^{-4}
\]

Thus, the equation becomes:
\[
3^{-4} = 3^x
\]

Since the bases are the same, we can equate the exponents:
\[
x = -4
\]

So, the solution is \(x = -4\).

---

Would you like more details or further explanation?

Here are five related questions:
1. What is the general approach for solving exponential equations?
2. How do you express other fractions as powers of integers?
3. What are the properties of exponents that help solve equations like this?
4. Can this method be applied to equations with different bases?
5. How does logarithmic transformation help when bases are not the same?

**Tip**: When solving exponential equations, always try to express both sides of the equation with the same base.

Learn how to solve the exponential equation 1/81 = 3^x with a detailed step-by-step explanation. This problem covers key algebraic concepts, such as powers of integers and the properties of exponents. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation