# how do you solve

Discussion in 'Mathematics' started by fudgesweets, Mar 3, 2011.

8^(-x)=8

2. ### fudgesweetsNew commenter

oops I meant how do you solve 8^(-x)=x

sorry

take logs

4. ### googolplexOccasional commenter

(in response to OP)

5. ### fudgesweetsNew commenter

tried that got

-xln8=lnx

ln8=-(lnx) / x

where to go from here?...

6. ### weebecka

Graph y=8^(-x) and see where it crosses y=x
I preferred your first question though!

7. ### googolplexOccasional commenter

Like I said, in response to OP.

8. ### DMNew commenter

You are not going to be able to "solve" it. You can use numerical methods to find an approximate answer.
The simplest way is to spot the solution lies between 0 and 1 (sign change) and then type either 0 or 1 or something inbetween into a calculator, press = and then type 8 ^ -ANS = and keep pressing = until the desired accuracy is obtained. This converges very slowly so a different method would be preferable.

9. ### DMNew commenter

A better method might be to identify the root between 0 and 1 and use Newton Raphson.
f(x) = x - 8^(-x)
f'(x) = 1 + ln (8) * 8^(-x)
Type 1 into calc and press =
Type ANS - (ANS - 8^(-ANS))/(1 + ln(8) * 8^(-x)) =
Press = about three more times.
Done.

10. ### DMNew commenter

Corrected a missing ANS.