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

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

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log_{3}(x^{log_{3}(x)})=4

lo g_{3} (x^{l o g_{3} (x)}) = 4

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

Solution steps

lo g_{3} (x^{l o g_{3} (x)}) = 4

Apply exponent rules

lo g_{3} (e^{l o g_{3} (x) l n (x)}) = 4

Rewrite the equation with

e^{l o g_{3} (x) l n (x)} = u

lo g_{3} (u) = 4

Solve

lo g_{3} (u) = 4 : u = 81

u = 81

Substitute back

u = e^{l o g_{3} (x) l n (x)},

solve for

x

Solve

e^{l o g_{3} (x) l n (x)} = 81 : x = 9, x = \frac{1}{9}

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

Verify Solutions:

x = 9

True

, x = \frac{1}{9}

True

The solutions are

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

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7^{x} = 4

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