What is the answer to log_{3}(x)-log_{x}(9)=0 ?

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

Solve for x: log_{3}(x)-log_{x}(9)=0

The solution is x=3^{sqrt(2)},x= 1/(3^{sqrt(2))}

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lo g_{3} (x) - lo g_{x} (9) = 0

x = 3^{2}, x = \frac{1}{3 ^{2}}

Decimal Notation

x = 4.72880 \dots, x = 0.21146 \dots

Solution steps

lo g_{3} (x) - lo g_{x} (9) = 0

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

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

Solve

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

u = 2, u = - 2

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

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

Solve

lo g_{3} (x) = - 2 : x = \frac{1}{3 ^{2}}

x = 3^{2}, x = \frac{1}{3 ^{2}}

Verify Solutions:

x = 3^{2}

True

, x = \frac{1}{3 ^{2}}

True

The solutions are

x = 3^{2}, x = \frac{1}{3 ^{2}}

ln (T) = 1.56 + 0.82 \cdot ln (56)

lo g_{10} (5 k) = 10

- 6 = - ln ((0)^{2} + c_{1})

lo g_{3 x + 2} (8) = lo g_{5} (2)

lo g_{b} (3) = 10

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