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

The answer to log_{3}(x)+log_{x}(3)=-2 is x= 1/3

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

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

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

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 = \frac{1}{3}

x = \frac{1}{3}

Verify Solutions:

x = \frac{1}{3}

True

The solution is

x = \frac{1}{3}

lo g_{4} (x + 3) = lo g_{4} (9)

lo g_{2} (x^{3}) + lo g_{2} (2) = 4

lo g_{5} (4 x - 3) = 1

lo g_{5} (4 x - 3) = 2

4 = 2 + ln (x - 1)

What is the answer to log_{3}(x)+log_{x}(3)=-2 ?
The answer to log_{3}(x)+log_{x}(3)=-2 is x= 1/3
Solve for x: log_{3}(x)+log_{x}(3)=-2
The solution is x= 1/3