What is the answer to x^{4+log_{3}(x)}= x/9 ?

The answer to x^{4+log_{3}(x)}= x/9 is x= 1/3 ,x= 1/9

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x^{4+log_{3}(x)}= x/9

x^{4 + l o g_{3} (x)} = \frac{x}{9}

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

Decimal

x = 0.33333 \dots, x = 0.11111 \dots

Solution steps

x^{4 + l o g_{3} (x)} = \frac{x}{9}

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

(4 + u) u = u - 2

Solve

(4 + u) u = u - 2 : u = - 1, u = - 2

u = - 1, u = - 2

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

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

Solve

lo g_{3} (x) = - 2 : x = \frac{1}{9}

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

Verify Solutions:

x = \frac{1}{3}

True

, x = \frac{1}{9}

True

The solutions are

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

lo g_{5} (x^{2} + x + 4) = - 3

lo g_{\frac{1}{7}} (x) = - 3

lo g_{10} (x) + lo g_{10} (2) = 5

lo g_{x + 6} (2 x^{2} + 8) = 2

w, q = 2 ln (\frac{w}{2 p})

What is the answer to x^{4+log_{3}(x)}= x/9 ?
The answer to x^{4+log_{3}(x)}= x/9 is x= 1/3 ,x= 1/9
Solve for x: x^{4+log_{3}(x)}= x/9
The solution is x= 1/3 ,x= 1/9