Question

Solve for x
(x-2)^-4=625

Answer 1

Is this a log question?

Answer 2

no

Answer 3

(x-2)^4=625
= (x^4 + 16) = 625
x^4 = 609
x= 5

Answer 4

I got 7 I am really confused

Answer 5

that (x-2)^4 is -4 not 4

Answer 6

How did you get 7? What's your working?

Answer 7

(x-2)=625^(1/4)
x-2=5
x=7

Answer 8

Can someone help me please

Answer 9

Oh my bad, I forgot to put the negative before the 4. Then yep, 7 is the answer!

Answer 10

Actually no

Answer 11

you're supposed to solve what's in the bracket first.

Answer 12

you can't bring the ^4 to the other side.

Answer 13

\[(x-2)^{-4}=625\]

Answer 14

oh ok but then x=7 is correct

Answer 15

No it would not be. If x = 7 the answer would be 0.016, not 625.

Answer 16

I am really confused

Answer 17

You have to first solve what's in the brackets. So (x-2) ^-4

Answer 18

ok got that then I have x^-4 then what

Answer 19

this \((x-2)^{-4}\) means this \(\frac{1}{(x-2)^4}\)

Answer 20

you have
\[\frac{1}{(x-2)^4}=625\] so
\[(x-2)^4=\frac{1}{625}\]

Answer 21

Yes^, but this means there are real and complex answers.?

Answer 22

that means
\[x-2=\pm\frac{1}{5}\]

Answer 23

if
\[x-2=-\frac{1}{5}\] then
\[x=-\frac{1}{5}+2=\frac{9}{5}\] and if
\[x-2=\frac{1}{5}\] then
\[x=\frac{1}{5}+2=\frac{11}{5}\]

Answer 24

so your two answers are
\[x=\frac{9}{5}\] or
\[x=\frac{11}{5}\]

Answer 25

and 2 - i/5
2 + i/5 if you want the complex parts