To solve the equation \( 7.92 = 10^{-X} \), we need to isolate \( X \).

### Step 1: Take the logarithm of both sides
We'll use the common logarithm (base 10) since the equation involves a power of 10.

\[
\log(7.92) = \log(10^{-X})
\]

### Step 2: Apply the logarithm power rule
The logarithm power rule states that \( \log(a^b) = b \cdot \log(a) \). Applying this rule to the right side:

\[
\log(7.92) = -X \cdot \log(10)
\]

Since \( \log(10) = 1 \), the equation simplifies to:

\[
\log(7.92) = -X
\]

### Step 3: Solve for \( X \)
Now, solve for \( X \):

\[
X = -\log(7.92)
\]

### Step 4: Calculate the value
Using the logarithm:

\[
X = -\log(7.92) \approx -0.898
\]

So, the solution is:

\[
X \approx -0.898
\]

Would you like more details or have any other questions? 

Here are 5 related questions:

1. How do you solve equations involving logarithms of different bases?
2. What are the properties of logarithms that are useful in solving equations?
3. How can logarithmic functions be used to model real-world scenarios?
4. What is the difference between natural logarithms and common logarithms?
5. How does the change of base formula work in logarithms?

**Tip:** Always remember that the logarithm of a number less than 1 is negative, which can be useful when solving logarithmic equations.

Learn how to solve the exponential equation 7.92 = 10^(-X) using logarithms. This problem involves logarithmic functions and the logarithm power rule, and it explains how to isolate X step-by-step. Suitable for students in Grades 10-12.

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