Question

1/256=16^x-9 Can someone please show me how to solve this?

Answer 1

Is this your question
\[\large\frac{1}{256}=16^{x-9}\]

Answer 2

??

Answer 3

Yes it is.

Answer 4

Ok tell me what's the power of 2 so that we get 256
\[2^y=256\]
or find y?

Answer 5

1/256 = 16^(x -9)
1/4^4 = 4^2(x - 9)
1/4^4 can be written as 4^-4 using the laws of indices
=> 4^-4 = 4^2(x - 9)
Since the bases are the same, they cancel out leaving:
-4 = 2(x - 9)
-4 = 2x - 18
-4 + 18 = 2x
14 = 2x
x = 7

Answer 6

Thank you so much!