Question

(1/7)^4-2x = √7, find x. ​

Answer 1

Answer:

How can I solve this equation: 72x+1−2(7)x+1=−7 ?

Let’s solve for x :

72x+1−2∗7x+1=7(7x)2−14∗7x=−7

Making the substitution z=7x we get :

7z2−14z=−7

Dividing by 7 :

z2−2z=−1

z2−2z+1=0

(z−1)2=0

z−1=0

z=1

Substituting back for z=7x :

7x=1

or equivalently

7x=70

Equating on both sides the exponents of 7 we get :

x=0

Below is a plot of the real solution as the point of intersection of two curves (made with Mathematica and a little Photoshop):

That was the real valued solution. The more general complex valued solution can be found by writing :

7x=1=e2iπn , with n∈Z

Taking the natural logarithm of both sides :

ln(7x)=ln(e2iπn)

xln(7)=2iπn

x=2iπnln(7),n∈Z