What is the answer to 9x^{log_{3}(x)}-x^3=0 ?

The answer to 9x^{log_{3}(x)}-x^3=0 is x=9,x=3

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9x^{log_{3}(x)}-x^3=0

Solution

9 x^{l o g_{3} (x)} - x^{3} = 0

Solution

x = 9, x = 3

Solution steps

9 x^{l o g_{3} (x)} - x^{3} = 0

Add

x^{3}

to both sides

9 x^{l o g_{3} (x)} - x^{3} + x^{3} = 0 + x^{3}

Simplify

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

Popular Examples

log_{3}((r+4)^2)=2

lo g_{3} ((r + 4)^{2}) = 2

1*15=log_{10}(x)

1 \cdot 15 = lo g_{10} (x)

log_{4}(x)+log_{2}(x)=12

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

log_{10}(x)=-2.9

lo g_{10} (x) = - 2.9

log_{10}(x)=-2.8

lo g_{10} (x) = - 2.8

Frequently Asked Questions (FAQ)

What is the answer to 9x^{log_{3}(x)}-x^3=0 ?
The answer to 9x^{log_{3}(x)}-x^3=0 is x=9,x=3
Solve for x: 9x^{log_{3}(x)}-x^3=0
The solution is x=9,x=3

9x^{log_{3}(x)}-x^3=0

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to 9x^{log_{3}(x)}-x^3=0 ?

Solve for x: 9x^{log_{3}(x)}-x^3=0