if 3^x + 4^x + 7^x = 16 what is the value of x?
please full solution!
2007-03-06 00:09:13 · 7 answers · asked by pradip 1 in Science & Mathematics ➔ Mathematics
And kindly ignore Titan's answer as well: ln (a+b) ≠ ln a + ln b. It is easy to show that no value of x less than 1 can possibly suffice, since for x<1, 3^x + 4^x + 7^x < 3+4+7 = 14 < 16.
This problem cannot be solved algebraically, so we must resort to numerical solutions. Simple binary search yields a solution at x≈1.082954248383663. This was done in about as much time as it took to type in the function using a free computer algebra system called maxima, which may be downloaded from http://maxima.sourceforge.net/ . The command used was find_root(3^x + 4^x + 7^x - 16, x, 1, 2); .
2007-03-06 01:24:01 · answer #1 · answered by Pascal 7 · 0⤊ 1⤋
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2016-12-18 06:49:33 · answer #2 · answered by Anonymous · 0⤊ 0⤋
x=16/14
2007-03-06 00:14:19 · answer #3 · answered by tintin 2 · 0⤊ 3⤋
14x=16
x=14/16=7/8
2007-03-06 00:15:06 · answer #4 · answered by Dave aka Spider Monkey 7 · 0⤊ 3⤋
Ignore those answers that think that ^ is the same as * , ok?
2007-03-06 00:23:27 · answer #5 · answered by pjjuster 2 · 0⤊ 2⤋
you will have to do this using logarithms.
xlog3+xlog4+xlog7=log16
x(log3+log4+log7)= log16
x= log16/log3+log4+log7
x= 1.20411/0.4771+0.6021+0.8450
x=1.20411/1.9242
x=0.62577
2007-03-06 00:19:20 · answer #6 · answered by Titan 4 · 2⤊ 2⤋
if it's simple, then why can't you answer it? please be attentive in class. don't use us to solve your homework.
2007-03-06 00:18:43 · answer #7 · answered by swirlz 2 · 0⤊ 3⤋