x=2.66
i plugged it in my graphing calculator
Solve 2x+1=2^x to find the other (not 0,1) intersection. Truly vexing. Thanks.
4 answers
Yeah, I can get the same x value if I use a grapher s/w but I need to solve it mathematically. Well, "need" is a bit extreme. I just "want" to solve this purely for intellectual purposes. Thanks.
I noticed your post was basically left unanswered.
To solve your equation requires some rather sophisticated math.
I used "Newton's Method" to solve it.
Newton's Method can be summarized by :
newx = x - f(x)/f'(x)
for yours:
newx = x -(ln2(2^x) - 2x - 1)/(ln2(2^x)-2)
you would then start with a reasonable guess as an answer. I went with x=2
and my newx was 2.360674
now make that your x and sub again.
The x value you just used and the newx should approach each other.
after 11 steps of doing this on my calculator I had x = 2.62975
sub that back into your equation gives me
Left side = 6.3195
Right side = 6.31923 , not bad
If you need more accuracy, just keep repeating the process until your calculator shows the same output as input, ( x = newx)
Newton's Method has been known for hundrreds of years, (Isaac Newton 1643-1727)
but only since the advent of scientific calculators has it become really practical.
To solve your equation requires some rather sophisticated math.
I used "Newton's Method" to solve it.
Newton's Method can be summarized by :
newx = x - f(x)/f'(x)
for yours:
newx = x -(ln2(2^x) - 2x - 1)/(ln2(2^x)-2)
you would then start with a reasonable guess as an answer. I went with x=2
and my newx was 2.360674
now make that your x and sub again.
The x value you just used and the newx should approach each other.
after 11 steps of doing this on my calculator I had x = 2.62975
sub that back into your equation gives me
Left side = 6.3195
Right side = 6.31923 , not bad
If you need more accuracy, just keep repeating the process until your calculator shows the same output as input, ( x = newx)
Newton's Method has been known for hundrreds of years, (Isaac Newton 1643-1727)
but only since the advent of scientific calculators has it become really practical.
Wow! Cheers. I'll look up on it. But, basically, there's no way to simplify that "equation" to something like x=... ? I was thinking along the lines of using Log, but I can't simplify log(2x-1) :(
Again, cheers.
Again, cheers.