What is the answer to 2log_{x}(3)-log_{3}(x)+1=0 ?

The answer to 2log_{x}(3)-log_{3}(x)+1=0 is x= 1/3 ,x=9

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2log_{x}(3)-log_{3}(x)+1=0

2 lo g_{x} (3) - lo g_{3} (x) + 1 = 0

x = \frac{1}{3}, x = 9

Decimal Notation

x = 0.33333 \dots, x = 9

Solution steps

2 lo g_{x} (3) - lo g_{3} (x) + 1 = 0

Apply log rules

\frac{2}{lo g _{3} ( x )} - lo g_{3} (x) + 1 = 0

Rewrite the equation with

lo g_{3} (x) = u

\frac{2}{u} - u + 1 = 0

Solve

\frac{2}{u} - u + 1 = 0 : u = - 1, u = 2

u = - 1, u = 2

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = - 1 : x = \frac{1}{3}

Solve

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

x = \frac{1}{3}, x = 9

Verify Solutions:

x = \frac{1}{3}

True

, x = 9

True

The solutions are

x = \frac{1}{3}, x = 9

lo g_{e} (x) = 2

ln (x - 2) + ln (12 - x) = 0

lo g_{8} (x - 5) = \frac{2}{3}

lo g_{10} (x + ln (x)) = 1

lo g_{5} (4 x) = 2

What is the answer to 2log_{x}(3)-log_{3}(x)+1=0 ?
The answer to 2log_{x}(3)-log_{3}(x)+1=0 is x= 1/3 ,x=9
Solve for x: 2log_{x}(3)-log_{3}(x)+1=0
The solution is x= 1/3 ,x=9