How do you solve 9 to the power of x equals 243?

Answer 1

9x = 243

ln(9x) = ln(243)

xln(9) = ln(243)

x = ln(243)/ln(9)

x = 2.5

NB this works with log10 too.

NBB if you don't have a calculator, this kinda question will only have easy values of x like integer values or 0.5, so its always worth chucking numbers in.

Answer 2

To solve the equation 9^x = 243, we need to rewrite 243 as a power of 9. Since 243 = 3^5, we can express it as 9^2 = 3^5. Therefore, the equation becomes 9^x = 9^2. By equating the exponents, we get x = 2. Thus, the solution to the equation is x = 2.

Answer 3

Well, isn't that a happy little math problem we have here? To solve 9 to the power of x equals 243, we can rewrite 243 as 3 to the power of 5. Since 9 is 3 squared, we can rewrite 9 as 3 to the power of 2. Now we have 3 to the power of 2x equals 3 to the power of 5. So, setting the exponents equal to each other, we get 2x equals 5. Therefore, x equals 5 divided by 2, which simplifies to x equals 2.5. Happy solving!

Answer 4

Oh, dude, solving 9 to the power of x equals 243 is like trying to find your keys in a messy room - annoying but doable. So, you're basically asking what power you need to raise 9 to in order to get 243. Well, guess what? x is 3 because 9 to the power of 3 is indeed 243. Easy peasy, lemon squeezy!