Asked by Sam
Find x
(4^x)=((3/4)x)+7
Thank you!
(4^x)=((3/4)x)+7
Thank you!
Answers
Answered by
Reiny
Woahhh! you are going to need some fancy work here
let's look at y = x^4 vs y = 3x/4 + 7
https://www.wolframalpha.com/input/?i=plot+y+%3D+4%5Ex+,+y+%3D+3x%2F4+%2B+7
looks like we have 2 solutions, one between -9 and -10 and another around 1.5
Do you know Calculus, thus Newton's Method?
let's look at y = x^4 vs y = 3x/4 + 7
https://www.wolframalpha.com/input/?i=plot+y+%3D+4%5Ex+,+y+%3D+3x%2F4+%2B+7
looks like we have 2 solutions, one between -9 and -10 and another around 1.5
Do you know Calculus, thus Newton's Method?
Answered by
oobleck
I suspect a typo. However, we can solve
4^x=3/4^x+7
Now, let u = 4^x and we have
u^2 - 7u - 3 = 0
u = (7±√61)/2
We want only the real solution:
u = (7+√61)/2
so, x = log<sub><sub>4</sub></sub> (7+√61)/2
or
x = (log (7+√61)/2)/log4
4^x=3/4^x+7
Now, let u = 4^x and we have
u^2 - 7u - 3 = 0
u = (7±√61)/2
We want only the real solution:
u = (7+√61)/2
so, x = log<sub><sub>4</sub></sub> (7+√61)/2
or
x = (log (7+√61)/2)/log4
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.