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

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

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

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

x = 2

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{2} (x) = u

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

Solve

\frac{1}{u} + 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_{x} (2) + lo g_{2} (x) = 0

x, ln (3 x - 13) = 3

ln (2 x) - ln (x^{2} - 3) = 0

lo g_{10} (x^{3} + 200) = 2

x, ln (x) = - (3 y + ln (y))

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