## sammysweets 3 years ago What is the solution to the equation 9^(x - 2) = 27 ? x = 2.5 x = 0.5 x = -0.5 x = 3.5

1. jim_thompson5910

Hint: rewrite 9 as 3^2 and 27 as 3^3

2. jim_thompson5910

Then you can say 9^(x - 2) = 27 (3^2)^(x - 2) = 3^3 3^(2(x-2)) = 3^3

3. sammysweets

4. jim_thompson5910

Check: 9^(x - 2) = 27 9^(2.5 - 2) = 27 ... plug in the *possible* solution x = 2.5 9^(0.5) = 27 3 = 27 The last equation is false, so x = 2.5 is NOT the answer

5. sammysweets

ahh i'm still confused.

6. jim_thompson5910

the bases are the same in 3^(2(x-2)) = 3^3 so the exponents are the same: 2(x-2) = 3

7. jim_thompson5910

what do you get when you solve 2(x-2) = 3

8. sammysweets

0...? i'm sorry. i'm really bad at math.

9. jim_thompson5910

that's ok, you'll get better with practice distribute to get 2(x-2) = 3 2x-4 = 3 what's next?

10. jasonxx

2x=7 x=7/2

11. sammysweets

am i just plugging in the answer choices for x?

12. jim_thompson5910

you can if you want to check (that's what I would do)

13. jim_thompson5910

btw, x = 7/2 is the same as x = 3.5

14. sammysweets

ohhh okay thank you so much.

15. samantha.m.

im so comfused I worked it out like this 9^(x-2)=27 3^2(x-2)=3^9 3^2x-4=3^9 2x-4=9 2x=13 13\2 x=6.5 but its not a choice. I have pluged in all of them and nothing im so condused. if anyone finds an answer please let me know

16. jim_thompson5910

27 is NOT equal to 3^9 you're thinking of 3 times 9 = 27 ------------------------------------------------------- It should be 27 = 3^3

17. Ziegenbein

its x=-0.5