Use the like bases property to solve the equation \( 10^{x}=10000 \) \( x=\square \)

To solve the equation \( 10^{x} = 10000 \), we first recognize that \( 10000 \) can be expressed as a power of \( 10 \). Since \( 10000 = 10^{4} \), we can rewrite the equation as \( 10^{x} = 10^{4} \). Now that we have like bases, we can set the exponents equal to each other: \[ x = 4 \] So the solution to the equation is \( x = 4 \). Additionally, it's helpful to remember that converting numbers into powers can simplify many equations. When you see large numbers, don’t shy away from breaking them down into their base forms—this is often the trick to finding the solution more quickly! You'll find many real-life applications of exponential equations—like calculating interest rates in finance or understanding trends in population growth. When you grasp the concept of like bases, you’re not just solving math problems; you’re also gaining tools for analyzing exponential growth in the world around you!