Question

(1/27)^x = 9^x-4
Hey (: I'm lost can someone help me figure this out?

Answer 1

I bet you mean
(1/27)^x=9^(x-4)

Answer 2

if so we can write both sides with base 3

Answer 3

yes

Answer 4

\[27=3^3 \\ \text{ so } \frac{1}{27}=3^{-3}\]

Answer 5

and I think you write 9 as 3^to something

Answer 6

after you do that just set exponents equal and solve for x

Answer 7

cool thank you!

Answer 8

you can show me any steps or show me what you get
and I can check it

Answer 9

I got 0=-4

Answer 10

\[(\frac{1}{27})^x=9^{x-4} \\ (3^{-3})^x=3^{2(x-4)} \\ 3^{-3x}=3^{2(x-4)}\]
so you did this right?

Answer 11

and then since you had the same base on both sides
you just needed to solve
-3x=2(x-4) for x

Answer 12

oh I tried x=x-4

Answer 13

no you have to get the same base on both sides before you can set exponents equal

Answer 14

\[a^x=a^y \text{ \implies } x=y \]

Answer 15

8/5?

Answer 16

that sounds totally better

Answer 17

haha thank you for your help! :)

Answer 18

np