What is the answer to x^{5-log_{3}(x)}=9x^2 ?

The answer to x^{5-log_{3}(x)}=9x^2 is x=3,x=9

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x^{5-log_{3}(x)}=9x^2

x^{5 - l o g_{3} (x)} = 9 x^{2}

x = 3, x = 9

Solution steps

x^{5 - l o g_{3} (x)} = 9 x^{2}

Apply log rules

(5 - lo g_{3} (x)) lo g_{3} (x) = lo g_{3} (9) + 2 lo g_{3} (x)

Rewrite the equation with

lo g_{3} (x) = u

(5 - u) u = lo g_{3} (9) + 2 u

Solve

(5 - u) u = lo g_{3} (9) + 2 u : 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 = 3

Solve

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

x = 3, x = 9

Verify Solutions:

x = 3

True

, x = 9

True

The solutions are

x = 3, x = 9

\frac{1}{ln ( x )} = 0

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

- ln (\frac{1}{x}) = ln (x)

lo g_{2} (x^{3}) + lo g_{2} (x) = 16

0 = - ln (x)

What is the answer to x^{5-log_{3}(x)}=9x^2 ?
The answer to x^{5-log_{3}(x)}=9x^2 is x=3,x=9
Solve for x: x^{5-log_{3}(x)}=9x^2
The solution is x=3,x=9