What is the answer to log_{3}(x)+log_{x}(3)=2 ?

The answer to log_{3}(x)+log_{x}(3)=2 is x=3

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log_{3}(x)+log_{x}(3)=2

lo g_{3} (x) + lo g_{x} (3) = 2

x = 3

Solution steps

lo g_{3} (x) + lo g_{x} (3) = 2

Apply log rules

lo g_{3} (x) + \frac{1}{lo g _{3} ( x )} = 2

Rewrite the equation with

lo g_{3} (x) = u

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

Solve

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

u = 1

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = 1 : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

- 6 + lo g_{10} (6 v) = - 7

4.35 = 3 - lo g_{10} (x)

lo g_{3} (x) = lo g_{9} (3 x - 2)

lo g_{a} (49) = \frac{2}{3}

lo g_{x - 3} (2 x^{2} - 11 x + 16) = 2

What is the answer to log_{3}(x)+log_{x}(3)=2 ?
The answer to log_{3}(x)+log_{x}(3)=2 is x=3
Solve for x: log_{3}(x)+log_{x}(3)=2
The solution is x=3