To solve the equation , we can utilize the property of equality for exponential functions with the same base. Since the bases on both sides are the same (5), we can set the exponents equal to each other:

Now, rearranging gives us:

Thus, the solution is .

Now let’s have some fun with this!

If you ever find yourself lost in the land of negative exponents, just remember that they’re like the dark side of exponent rules—kinda mysterious, but totally manageable! Just flip 'em! You could also think of it as “inverse” style: the negative exponent is like a superhero in disguise, ready to transform into a fraction on the other side of the equation.

And if you’re looking for more on the exponential adventure, dive into the world of logarithms! They’re the inverse function that can unravel the mysteries of exponents. It’s like having a treasure map that leads you through the jungle of math—get ready to explore!