If 5^(x)=999, then the value of 5^(x-3) is

Given that \( 5^x = 999 \), we want to find the value of \( 5^{x-3} \).

To solve this, we can express \( 5^{x-3} \) in terms of \( 5^x \):

\[
5^{x-3} = \frac{5^x}{5^3}
\]

We already know that \( 5^x = 999 \). Therefore:

\[
5^{x-3} = \frac{999}{5^3}
\]

Now, calculate \( 5^3 \):

\[
5^3 = 125
\]

So:

\[
5^{x-3} = \frac{999}{125}
\]

Now, divide 999 by 125:

\[
5^{x-3} = 7.992
\]

So, the value of \( 5^{x-3} \) is approximately **7.992**.

Would you like more details or have any questions? Here are five related questions you might explore:

1. What is the value of \( 5^{x+2} \) if \( 5^x = 999 \)?
2. How would you solve for \( x \) if \( 5^x = 999 \)?
3. What would \( 5^{x-2} \) equal if \( 5^x = 999 \)?
4. How do logarithms help in solving equations like \( 5^x = 999 \)?
5. How can you use \( 5^x = 999 \) to find \( 5^{2x} \)?

**Tip:** Remember that exponent rules are powerful tools for transforming and solving exponential equations.

Learn how to find the value of 5^(x-3) when given that 5^x equals 999. This problem involves using exponent rules and division of exponents to solve for the required value. Suitable for advanced high school students.

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