Before watching: This is actually fairly easy. Bear in mind that 16^2x >0 for all real X, and that on the left we have nested numbers in square roots. Thus, we will be skipping over any negative square roots; if we're meant to consider complex solutions, then we should analyze those more thoroughly. Meantime, though, we do our square roots on the left innermost-to-outermost. √(2√(16√16)) = √(2√64) = √(2*8) = √16 = 4 Then 4 = 16^(2z). 4= 2^x, 16 = 2^4, and a^(mn) = (a^m)^n Then 2^2 - (2^4)^(2x_ = 2^(8x) Thus 2 = 8x, and thus x = 1/4.
Of course, you can travel from Paris to London via Honolulu, which is what the author of this video suggests. Everything is solved in the mind! Everything on the left under the radical signs ends up being 4. (I don't think anyone doesn't know that the square root of 16 is 4 and the square root of 4 is 2). Further, 4 is 16 to the power of 1/2. We equate the degrees of expressions on the right and left and get 1/2 = 2x, from where x = 1/4. That's all!
You hv taken a long method to find the solution. Sqrt 2 *sqrt of 16*sqrt of 16= ( 2^4)^2x Sqrt of 2* sqrt of 16*4 = RHS Sqrt of 2 * 8= RHS sqrt of 16 = RHS 4= (2^4)^2x Or, 2^2= (2^8x) Or, 2= 8x Then x=2/8 or 1/4.
Зачем усложнять себе решение? Возводить 16 в квадрат Если учесть что 16 =4^2, 16*4=8^2 То в итоге 4=16^2х 2х=1/2 х=1/4 2 минуты на решение, а не 8 минут
Excellent
Before watching:
This is actually fairly easy. Bear in mind that 16^2x >0 for all real X, and that on the left we have nested numbers in square roots. Thus, we will be skipping over any negative square roots; if we're meant to consider complex solutions, then we should analyze those more thoroughly.
Meantime, though, we do our square roots on the left innermost-to-outermost.
√(2√(16√16)) = √(2√64) = √(2*8) = √16 = 4
Then 4 = 16^(2z). 4= 2^x, 16 = 2^4, and a^(mn) = (a^m)^n
Then 2^2 - (2^4)^(2x_ = 2^(8x)
Thus 2 = 8x, and thus x = 1/4.
1/4
Of course, you can travel from Paris to London via Honolulu, which is what the author of this video suggests. Everything is solved in the mind! Everything on the left under the radical signs ends up being 4. (I don't think anyone doesn't know that the square root of 16 is 4 and the square root of 4 is 2). Further, 4 is 16 to the power of 1/2. We equate the degrees of expressions on the right and left and get 1/2 = 2x, from where x = 1/4. That's all!
Oui bien sur !
2^1/2×16^1/4×16^1/8=16^2×
2^1/2×2×2^1/2=2^8×
2^2=2^8×
8x=2
×=1/4
x =1/4
You hv taken a long method to find the solution.
Sqrt 2 *sqrt of 16*sqrt of 16= ( 2^4)^2x
Sqrt of 2* sqrt of 16*4 = RHS
Sqrt of 2 * 8= RHS
sqrt of 16 = RHS
4= (2^4)^2x
Or,
2^2= (2^8x)
Or,
2= 8x
Then x=2/8 or 1/4.
Very long winded. Just evaluate sq rt side. Comes to 4. Then rhs. Which comes to 4 power 4x. So 4 power 1. =. 4power 4x. Same base so 1= 4x. X=1/4
oui c'est plus simple.
X=1/4
X=1/2 (may be
Зачем так сложно. Это вычисляется устно. Корень из 16 равен 4 + свойства корней
2^2=2^8x
8x=2
X=2/8=1/4
For such a simple equation a DAMN FOOL wastes 8.5 minutes.I solved it orally with in a half minute.
2^(1/2)×16^(1/4)×16^(1/8)=16^(2X)
2^(1/2+4/4+4/8)=4^(4X)
2^((4+8+4)/8)=4^(4X)
2^2=4^(4X)
4^1=4^(4X)
1=4X
X=1/4
Ouf que c'est lourd !
√16 = 4 donne de tête:
√(2.√(16√16)) = 16^(2x)
√(2.√(16.4)) = (4²)^(2x)
√( 2.(4.2) ) = (4)^(4x)
√(16) = (4)^(4x)
4 = (4)^(4x)
4x = 1 x = 1/4
COULD HAVE BEEN DONE MORE SIMPLY.
MUSIC IS DISASTROUS.
Unnecessarily made lenthy
Зачем усложнять себе решение? Возводить 16 в квадрат
Если учесть что 16 =4^2, 16*4=8^2
То в итоге
4=16^2х
2х=1/2
х=1/4
2 минуты на решение, а не 8 минут
X =1/4