# Solve the trigonometric equation

Razy
Visitor
2016-06-26 18:30:27
#1
I don't know how to solve this eq:
$\frac{cos(log_{2} x)\cdot 2^{\sqrt{4-x}}}{\sqrt{2x-1}}=0$

## RE: Solve the trigonometric equation

Pixar
Visitor
2016-06-26 18:43:06
#2
First you need to put the conditions:
x > 0 for log
4-x ? 0 for first radical => x ? 4
2x-1 > 0 for the sec radical => x
So, we get
x ∈ (1/2;4]

And now, the equations become: $cos(\log _{2}x)\cdot 2^{\sqrt{4-x}}=0$
$cos(\log _{2}x)=0$
$\log _{2}x=0 + 2k\pi , \: \: k\in \mathbf{Z}$
But here we have to consider k = 0 and we have
x = 1 ∈ (1/2;4]
So 1 is a good solution