Question 16 Use the like bases property to solve the equation \( 2^{x}=128 \) \( x=\square \)

To solve \( 2^{x}=128 \), we first rewrite 128 as a power of 2. We know that \( 128 = 2^7 \), so we can rewrite the equation as \( 2^{x} = 2^{7} \). With like bases, we can set the exponents equal to each other, giving us \( x = 7 \). Remember, it's always handy to express numbers in terms of their prime factorization when dealing with exponential equations. This not only makes your math journey smoother but also helps in visualizing how different exponents relate to one another. In real-world applications, understanding exponents and their properties can be quite useful. For example, if you're working in finance and trying to find out how long it takes for an investment to double, the mathematics of exponential growth comes into play. Using the like bases property will help you tackle these exponential equations efficiently!