2^x + 2^-x = 5/4 ... what is x?
912352
I believe the answer should be \n\nlog{ [ 5 +/- sqrt(39)i ]/8} / log 2.\n\nSteps are as follows:\n\n2^x + 1/2^x = 5/4\n(2^x * 2^x + 1)/2^x = 5/4\n4(2^x * 2^x + 1) = 5 * 2^x\n4 * 2^x * 2^x + 4 = 5 * 2^x\n4(2^x)^2 - 5(2^x) + 4 = 0\n\nlet 2^x be y\n\n4y^2 - 5y + 4 = 0\n\nsolve it by the equation, you get\n\ny = [5 +/- sqrt(25 - 4*4*4) ]/2*4\ny = [5 +/- sqrt(-39) ]/8\n\nsince y = 2^x\n\n2^x = [5 +/- sqrt(-39) ]/8\nxlog(2) = log {[5 +/- sqrt(-39) ]/8}\nx = log {[5 +/- sqrt(-39) ]/8} / log (2)\nor\nx = log {[5 +/- sqrt(39)i ]/8} / log (2)
858963
The answer is actually much more complex than one would think! The correct answer though is ...\n\n((2^n)(n-.5)!)/(2(.5!))\n\nThat looks kind of messy, so in English that is "2 to the n times n minus 1 half factorial over 2 times 1 half factorial."\n\nPlugging in 1,3,5,7 for n on a graphing calculator, we get 1,3,15,105, which are the correct first four terms in the sequence.
284432
There is no sign for exponent in your question.  I assume you mean\n2^(3/5)\nAny expression of the from x^(m/n) can be written as the\nnth root of x^m\nThus, 2^(3/5) is the fifth root of 2^3 which simplifies to \nthe fifth root of 8.
883726
when multiplying, exponents with like bases add, therefore\nn+1+n-1 =2n and your answer is x^2n
824446
Not sure... but the answer is a complex number, I'll tell you that. There is no real solution for 5^x = x. In the equation a^x=x, a has to be less than e and greater than 0 for there to be a real solution.
635930
x+2/x-2 \n= (x^2 - 2x + 2)/x [BODMAS rule]\nSo Eric is correct.
447887
You probably mean\np(x) = 2x^4 +5x^3 – 3x^2 -2x -6\nThe answer is e) Both b,d\nbecause when you multiply the factors you should get the original expression and (x+3)(2x^3 –x^2 -2)= 2x^4 +5x^3 – 3x^2 -2x -6\nThis was quickly seen because you need x^4 which is only obtainable by x multiplied by x^3 in your problem :)\nHope this helps
982509
Let log2 5 = x\n\nThen 2^x must be 5\n\nTake log of both sides but use log10 (common log, on calculator)\n\nx log 2 = log 5\n\nDivide both sides by log 2
201432
x=2 and y =2,\n\n2^2=2^2 and 2*2 = 2 + 2 =4
812981
1/2^x < 0.01 \nthen multiply both sides by 2^x\n1 < 0.01 2^x\nnow divide both sides by 0,01:\n1/ 0.01 < 2^x\n100 < 2^x\n~
599364
x^2 + x = x(x+1)\n\nIt can be simplified to x(x+1).
920343
(4/3)[x^3/(2-x)]^(1/3)\n[(2-x)(3)x^2-x^3(-1)]/\n(2-x)^2=\n\n 4x[1/(2-x)]^(1/3)\n[3x^2(2-x)+x^3]/\n3(2-x)^2
774115
.x^2+5x+6/x+1=6\n\nassuming you mean:\n(x^2+5x+6) / (x+1)=6\n\nx^2+5x+6=6 (x+1)\nx^2 -x=0\nx(x-1)=0\nso x=0 or x=1
117989
do it like grade 5 - 1 see - \n[X-(1/5X)^2] sqrt\n    (1/5X)^2 \n     1/25 (2X) \n[X-1/25(2X)]sqrt\nX=4 , understand
678104
Are you trying to factor?\n\n2^(x+1) * 8^(-x)\n\nYou can solve this by remembering that a negative exponent term in the numerator should go into the denominator as a positive exponent term. Remember also that y^(x+1) = y*y^(x)\nand that 2^(x+1) with 8^x means that for any number, x, there is one more "2" than there are "8"\n\nThis is easily a homework question. You'll have to complete it from here.
789893
x+4(2x+1)=3( x-2)+10x : x=2.5\n\nI like to work with x
464723
X^1/2/(x^3/4)(x^-4) = x^-17/4\n\nX^1/2/((x^3/4)(x^-4)) = x^21/4\n\ndidnt really understand the question clearly, i interpret it two different ways. i think its right