# how do you solve

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

1. 8^(-x)=8

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

sorry

3. take logs

4. (in response to OP)

5. tried that got

-xln8=lnx

ln8=-(lnx) / x

where to go from here?...

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

7. Like I said, in response to OP.

8. 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. 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. Corrected a missing ANS.