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The given equation is:

\[
10^{x-3} = 10^5
\]

To solve for \( x \), we can use the property of equality of exponents. If the bases are equal, then the exponents must be equal. Thus:

\[
x - 3 = 5
\]

Now, solve for \( x \):

\[
x = 5 + 3 = 8
\]

So, the value of \( x \) is:

\[
x = 8
\]

Would you like a deeper explanation, or have any other questions? Here are some related questions for further practice:

1. What would be the value of \( x \) if the equation was \( 10^{x+2} = 10^4 \)?
2. How would you solve \( 10^{2x - 1} = 10^6 \)?
3. If the equation was \( 10^{3x - 5} = 10^2 \), what is \( x \)?
4. What property of exponents is used to equate the exponents when the bases are the same?
5. How would you solve \( 5^{x+4} = 5^7 \)?

**Tip:** Remember, when bases are equal, you can directly set the exponents equal to each other to solve for the variable.

Find the value of x that makes the statement true: 10^(x-3) = 10^5.

Learn how to solve the exponential equation 10^(x-3) = 10^5 using the law of exponents. This problem helps understand how to equate exponents when bases are the same. Suitable for students in Grades 9-10.

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