What is the answer to x^{2log_{9}(x)-1}=3sqrt(x) ?

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

Solve for x: x^{2log_{9}(x)-1}=3sqrt(x)

The solution is x=9,x= 1/(sqrt(3))

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x^{2 l o g_{9} (x) - 1} = 3 x

x = 9, x = \frac{1}{3}

Decimal Notation

x = 9, x = 0.57735 \dots

Solution steps

x^{2 l o g_{9} (x) - 1} = 3 x

Apply log rules

(2 lo g_{9} (x) - 1) lo g_{9} (x) = \frac{1}{2} lo g_{9} (x) + \frac{1}{2}

Rewrite the equation with

lo g_{9} (x) = u

(2 u - 1) u = \frac{1}{2} u + \frac{1}{2}

Solve

(2 u - 1) u = \frac{1}{2} u + \frac{1}{2} : u = 1, u = - \frac{1}{4}

u = 1, u = - \frac{1}{4}

Substitute back

u = lo g_{9} (x),

solve for

x

Solve

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

Solve

lo g_{9} (x) = - \frac{1}{4} : x = \frac{1}{3}

x = 9, x = \frac{1}{3}

Verify Solutions:

x = 9

True

, x = \frac{1}{3}

True

The solutions are

x = 9, x = \frac{1}{3}

lo g_{4} (x^{2} - 6) = lo g_{4} (10)

lo g_{x} (25) = 5

ln (2 x) = 1

ln (9 x + e) = 9

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

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