What is the answer to log_{2}(x)+log_{x}(2)=2 ?

The answer to log_{2}(x)+log_{x}(2)=2 is x=2

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log_{2}(x)+log_{x}(2)=2

lo g_{2} (x) + lo g_{x} (2) = 2

x = 2

Solution steps

lo g_{2} (x) + lo g_{x} (2) = 2

Apply log rules

lo g_{2} (x) + \frac{1}{lo g _{2} ( x )} = 2

Rewrite the equation with

lo g_{2} (x) = u

u + \frac{1}{u} = 2

Solve

u + \frac{1}{u} = 2 : u = 1

u = 1

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 1 : x = 2

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

lo g_{16} (x) = \frac{1}{4}

lo g_{9} (y) = - \frac{1}{2}

lo g_{5} (x + 4) = 1 - lo g_{5} (x + 8)

lo g_{x} (\frac{16}{81}) = 4

lo g_{10} (2 x + 50) = 2

What is the answer to log_{2}(x)+log_{x}(2)=2 ?
The answer to log_{2}(x)+log_{x}(2)=2 is x=2
Solve for x: log_{2}(x)+log_{x}(2)=2
The solution is x=2