What is the answer to 2log_{3}(x)=log_{x}(9) ?

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

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2log_{3}(x)=log_{x}(9)

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

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

Decimal Notation

x = 3, x = 0.33333 \dots

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

2 u = \frac{2}{u}

Solve

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

u = 1, u = - 1

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

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

Solve

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

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

Verify Solutions:

x = 3

True

, x = \frac{1}{3}

True

The solutions are

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

lo g_{10} (x - 1) = 2

ln (x) + ln (x - 1) = 0

x ln (x) = 0

lo g_{6} (x + 3) + lo g_{6} (x + 4) = 1

2 lo g_{10} (x) - 1 = lo g_{10} (x - 1)

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