Question 5 Use the like bases property to solve the equation \( 5^{n+7}=5^{6 n-9} \) \( n= \) Question Help: Video Submit Question

When two exponentials with the same base are equal, you can set their exponents equal to each other. Here, you can simplify it to: \( n + 7 = 6n - 9 \). Rearranging that will lead you to combine like terms, giving you \( 7 + 9 = 6n - n \), which simplifies to \( 16 = 5n \), and ultimately, you find \( n = \frac{16}{5} \) or \( n = 3.2 \). Once you've got \( n \) in hand, it’s always a good idea to double-check your solution by plugging it back into the original equation. Doing the math, you'll find both sides equal \( 5^{10.2} \) confirming that your calculated value for \( n \) is indeed correct. It's like math magic, ensuring your solution is as solid as a rock!