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

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

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

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

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

Decimal Notation

x = 9, x = 0.33333 \dots

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

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

Solve

u - \frac{2}{u} = 1 : 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 = \frac{1}{3}

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

Verify Solutions:

x = 9

True

, x = \frac{1}{3}

True

The solutions are

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

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

lo g_{4} (x - 1) + lo g_{4} (x + 2) = 1

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

lo g_{x} (6 x - 8) = 2

ln (x + 3) = 4

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