Answer:
There is one solution and that answer is mixed number form 1 5/7 or exact form 12/7
Step-by-step explanation:
There are two of them.
I don't know a mechanical way to 'solve' for them.
One can be found by trial and error:
x=0 . . . . . 2^0 = 1 . . . . . 4(0) = 0 . . . . . no, that doesn't work
x=1 . . . . . 2^1 = 2 . . . . . 4(1) = 4 . . . . . no, that doesn't work
x=2 . . . . . 2^2 = 4 . . . . . 4(2) = 8 . . . . . no, that doesn't work
x=3 . . . . . 2^3 = 8 . . . . . 4(3) = 12 . . . . no, that doesn't work
<em>x=4</em> . . . . . 2^4 = <em><u>16</u></em> . . . . 4(4) = <em><u>16</u></em> . . . . Yes ! That works ! yay !
For the other one, I constructed tables of values for 2^x and (4x)
in a spread sheet, then graphed them, and looked for the point
where the graphs of the two expressions cross.
The point is near, but not exactly, <em>x = 0.30990693...
</em>If there's a way to find an analytical expression for the value, it must involve
some esoteric kind of math operations that I didn't learn in high school or
engineering school, and which has thus far eluded me during my lengthy
residency in the college of hard knocks.<em> </em> If anybody out there has it, I'm
waiting with all ears.<em>
</em>
This is a geometric sequence, so use the formula for the sum of a geometric sequence:
Sum = (a(r^n - 1))/(r - 1)
where a is the first term, -5
r is the common ratio, 5
and n is the number of terms
Thus,
Sum = ((-5)(5^6 - 1))/(5-1) = -19530
This is easy, if adding the first number to the second number you get 70.2 then if you want to find the middle number you will have to subtract 32.34 from 70.2 to get 37.86, now add that and 32.34 to check if it gives you 70.2.... When you add them you indeed get 70.2 so your work is correct meaning your middle number is 37.86
Hope this helped
I think that there are 4 termms if we condider onlu plus and minus as operators.
