Solve for the value of x that makes this a true statement:

10^6/10^x=10^2

2
6
8
4

1 answer

To solve the equation \( \frac{10^6}{10^x} = 10^2 \), we can use the properties of exponents.

First, we can rewrite the left side using the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \):

\[ \frac{10^6}{10^x} = 10^{6-x} \]

So the equation becomes:

\[ 10^{6-x} = 10^2 \]

Since the bases are the same, we can set the exponents equal to each other:

\[ 6 - x = 2 \]

Now, solve for \( x \):

\[ 6 - 2 = x \] \[ x = 4 \]

Thus, the value of \( x \) that makes the statement true is:

\[ \boxed{4} \]