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

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

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

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

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

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)

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

u = \frac{2}{u}

Solve

u = \frac{2}{u} : 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}}

lo g_{x} (16) = lo g_{2} (x)

ln (x) = \frac{6907756}{1000000}

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

4 + 2 lo g_{3} (x) = 17

4 ln (x) - 8 = 12

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