A Homemade Exponential Logarithmic Equation

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x^{log(x)/log(y)}=y^2-1
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PLAYLISTS 🎵 :

[djgiesz]

You can also use change of base to get x to the power log_x(y), which by definition means y, therefore y=y^2-1, and after solving the quadratic you can backsubstitute to solve for x

[gianpaolosoligo]

I used change of base in the exponent and simplified the base and the logarithm and solved the quadratic

[ManjulaMathew-wbzn]

Great job on finding y. I believe it’s worth mentioning something about x. Since the value of y is totally independent of x, it can be equal to any number other than 1.

[talberger]

you wrote "1st method", where is the 2nd one?

[jayantaboral]

Hi! It was pretty interesting. I think one more validation should be drawn from log y > 0 and log (y^2-1)>0 implying y>1. This is to further validate the solution y=(1+✓5)/2

[vimleshmaheshwari]

The simplest way x^ log y basex =y^2-1
y=y^2-1
y^2-y-1=0

[toastercoder]

2:07 did you notice that y^2-1>0? (this expression is inside a logarithm), y must be greater than 1

[sngmn]

change fraction to log_x(y), reduce exponent to "y" (its a LHS)
We got a quadratic y^2 - y - 1 = 0 and somewhere hidden golden

[bobbyheffley]

The golden ratio is the positive fixed point of f(x)=(x^2)-1.

[marklevin]

Left side is just y provided y>0 x>0 x is not equal 1
У=у^2-1 we need positive root

[srividhyamoorthy]

Finally at least something which is a bit challenging good work on your videos tho

[kevinmadden]

I also used Change of Base and got y equals(1+ sqrt(5))/2. How do you get x?

[scottleung]

I think after plugging in the golden ratio for y, x=10.

[vladimirkaplun]

How do you decide what might be complex and what must be purely real?

[sngmn]

Hey sybermath, mb you can stream with webcam?) We finally will see you)

[JeremyLionell]

So does that mean x can be anything other than 1 and the numbers below that?

[BlaqRaq]

Does this imply that life itself is irrational?
Since these values (e, pi, golden ratio) so special and also irrational.