This is made simple #maths #viral #mathematics #mathstricks #exponential #equation
Пікірлер: 20
@TheOldeCroweАй бұрын
Another approach: 8ˣ = x⁶ Taking the logarithm of both sides gives xln8 = 6ln|x| Using the power rule of logarithms gives x/ln|x| = 6/ln8 = 6/3ln2 = 2/ln2 and x/ln|x| = 2/ln2 = 4/2ln2 = 4/ln(2²) = 4/ln4 For x > 0, we have x/ln|x| = x/lnx so x/lnx = 2/ln2 and x/lnx = 4/ln4 which means that, for x > 0, there are two solutions: x = 2 and x = 4 Note that 8² = 2⁶ = 64 and 8⁴ = 4⁶ = 2¹² = 4096 For x < 0, we have x/ln|x| = x/ln(-x), so x/ln(-x) = 2/ln2 where, it turns out, there is a third solution: x ≈ -0.7666646959631231
@kemosabe761Ай бұрын
x=2 is only one of three solutions to this problem. 4 and ~-0.766665 are the others. I think you would be expected to demonstrate how to find these in an "Olympiad" question
If we imagine graphs of functions 8^x and x^6, it is clear that there should be at least 2 intersections at x0. Solution x=2. obviously, and you need to find the second one in the negative area. But it turns out there is a third solution!
@pukuluАй бұрын
x = 2 by inspection. Other solutions might be possible.
@nagarajabillurrao14 күн бұрын
Multiplying!
@phuocvlog9 күн бұрын
Easy to find x= 2 but are there any values for x? If we can prove f(x)=x^(1/x) is a monotonic function, we can say x=2 is only solution. However, this problem has many solutions, example x=4 is another solution
@mcmac802728 күн бұрын
It may help to consider revisiting some laws and rules in algebra specifically on identities of basic operations, i.e. 'cancellation of terms'. The art of 'rearranging' terms or their components takes practice using different approaches.
@mohinkhan250328 күн бұрын
❤❤❤❤❤❤❤❤❤❤❤
@GeorgeSickinger13 күн бұрын
The intuitive answer is 2…takes 30 seconds or less. This solution is like using a sledgehammer to crack a walnut
@emilaz280025 күн бұрын
It's easy I X=2
@user-eq2kc5pz6v3 күн бұрын
X= 2 or 4
@kinglamtsoi569613 күн бұрын
Why not take log both sides?🤔
@dardoburgos31792 күн бұрын
X= 2.
@2012tulio4 күн бұрын
Is this olympiad ?
@tungtranvu17623 күн бұрын
2^x = x^2 nhanh hơn
@pas6295Ай бұрын
Xis 2
@aurochrok63426 күн бұрын
2^3x = x^(3*2) => x=2. math olympiad my аss. stop the bs