9^x+1 = 81^x-9
solve the following exponential equation by expressing each side as a power of the same base and then equating exponents

Question

9^x+1 = 81^x-9 
solve the following exponential equation by expressing each side as a power of the same base and then equating exponents

mathteacher1729 · Answer

Do you mean:$$\huge 9^{x+1}=81^{x-9}$$

mertsj · Answer

Replace 9 with 3^2 and replace 81 with 3^4

anonymous · Answer

@mathteacher1729 yes thats what it is.

mathteacher1729 · Answer

Ok, in this case note that $\large 81=9^2$ and keep in mind the exponent rule $$\huge (a^{b})^c= a^{b\cdot c}$$so you can re-write the equation as

$$\huge 9^{x+1}=(9^{2})^{x-9}$$
and this means
$$\huge 9^{x+1}=9^{2(x-9)}$$

Now when it says "equate exponents" that means.. set the exponents equal to each other.  You can do this because their bases are the same. (the "bases are both 9). 

Can you figure out what to do next?

anonymous · Answer

im not sure if this is what i should do. but is it $$x+1=2x-18$$

mathteacher1729 · Answer

Yes, that's right. Now solve that equation and you'll have your value of x. 

When you find the value of x -- TEST IT OUT in the original equation to make sure!!

anonymous · Answer

@mathteacher1729 thank you SO MUCH!!!!!!

mathteacher1729 · Answer

Aww, thanks! :)