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Popular >

x^{ln(x)}=e

Solution

x^{l n (x)} = e

Solution

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

+1

Decimal Notation

x = 2.71828 \dots, x = 0.36787 \dots

Solution steps

x^{l n (x)} = e

Apply exponent rules

ln^{2} (x) = 1

Solve

ln^{2} (x) = 1 : x = e, x = \frac{1}{e}

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

Verify Solutions:

x = e

True

, x = \frac{1}{e}

True

The solutions are

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

Popular Examples

3^{x + 1} = 9^{x}

e^{0.1 t} = 3

2^{x+1}+(5)(2)^x=28

2^{x + 1} + (5) (2)^{x} = 28

4^{x+1}=16^{x-1}

4^{x + 1} = 1 6^{x - 1}

(sqrt(3))^x=27^{x-1}

(3)^{x} = 2 7^{x - 1}

Frequently Asked Questions (FAQ)

What is the answer to x^{ln(x)}=e ?
The answer to x^{ln(x)}=e is x=e,x= 1/e