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

The answer to 9\times x^{log_{3}(x)}=x^3 is x=9,x=3

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9\times x^{log_{3}(x)}=x^3

9 \cdot x^{l o g_{3} (x)} = x^{3}

x = 9, x = 3

Solution steps

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

Divide both sides by

9

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

Apply log rules

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

Rewrite the equation with

lo g_{3} (x) = u

uu = 3 u - 2

Solve

uu = 3 u - 2 : u = 2, u = 1

u = 2, u = 1

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

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

Solve

lo g_{3} (x) = 1 : x = 3

x = 9, x = 3

Verify Solutions:

x = 9

True

, x = 3

True

The solutions are

x = 9, x = 3

lo g_{2} (5 x) = 4

lo g_{0.5} (x) = 8

y, ln (x) = ln (y)

lo g_{10} (4 x) - lo g_{10} (12 + x) = 2

lo g_{10} (x) = 1.75

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