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

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

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

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

x = 1, x = 33

Solution steps

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

Apply log rules

3 lo g_{9} (x) = 4 lo g_{9} (x)^{2}

Rewrite the equation with

lo g_{9} (x) = u

3 u = 4 u^{2}

Solve

3 u = 4 u^{2} : u = 0, u = \frac{3}{4}

u = 0, u = \frac{3}{4}

Substitute back

u = lo g_{9} (x),

solve for

x

Solve

lo g_{9} (x) = 0 : x = 1

Solve

lo g_{9} (x) = \frac{3}{4} : x = 33

x = 1, x = 33

Verify Solutions:

x = 1

True

, x = 33

True

The solutions are

x = 1, x = 33

lo g_{4} (x) + lo g_{4} (x + 6) = 2

ln (x^{2}) = 20

lo g_{3} (4^{x}) = 1 - 2 x

lo g_{4} (x) = \frac{3}{2}

2 ln (x) = ln (x^{2})

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