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

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

Solve for x: 2log_{x}(3)=log_{3}(x)

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

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

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

Decimal Notation

x = 4.72880 \dots, x = 0.21146 \dots

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

\frac{2}{u} = u

Solve

\frac{2}{u} = 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}}

(\frac{5000}{70000}) = ln (x)

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

ln (2 x) = 16

lo g_{2} ((x + 1)^{3}) = 3

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

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