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

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

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

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

x = 9, x = 3

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

\frac{2}{u} + u - 3 = 0

Solve

\frac{2}{u} + u - 3 = 0 : u = 2, u = 1

u = 2, u = 1

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

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

Solve

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

x = 9, x = 3

Verify Solutions:

x = 9

True

, x = 3

True

The solutions are

x = 9, x = 3

1.5 = lo g_{10} (x)

0.85 = - lo g_{10} (x)

- lo g_{10} (x) = 1.5

lo g_{2} (x - 6) = 4

lo g_{2} (x - 6) = 3

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