What is the answer to x^{log_{3}(x)}=81 ?

The answer to x^{log_{3}(x)}=81 is x=9,x= 1/9

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x^{log_{3}(x)}=81

x^{l o g_{3} (x)} = 81

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

Solution steps

x^{l o g_{3} (x)} = 81

Apply exponent rules

lo g_{3} (x) ln (x) = ln (81)

Solve

lo g_{3} (x) ln (x) = ln (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}

4^{2 x} = 8^{x + 2}

(\frac{1}{4})^{x} = \frac{1}{64}

e^{2 x} + e^{x} = 4

2^{x - x^{2}} = 1

3^{3 x} = 2 7^{2 x + 3}

What is the answer to x^{log_{3}(x)}=81 ?
The answer to x^{log_{3}(x)}=81 is x=9,x= 1/9
Solve for x: x^{log_{3}(x)}=81
The solution is x=9,x= 1/9