What is the answer to x^{log_{10}(x)}=1000 ?

The answer to x^{log_{10}(x)}=1000 is x=10^{sqrt(3)},x= 1/(10^{sqrt(3))}

Solve for x: x^{log_{10}(x)}=1000

The solution is x=10^{sqrt(3)},x= 1/(10^{sqrt(3))}

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x^{l o g_{10} (x)} = 1000

x = 1 0^{3}, x = \frac{1}{1 0 ^{3}}

Decimal Notation

x = 53.95737 \dots, x = 0.01853 \dots

Solution steps

x^{l o g_{10} (x)} = 1000

Apply exponent rules

lo g_{10} (x) ln (x) = ln (1000)

Solve

lo g_{10} (x) ln (x) = ln (1000) : x = 1 0^{3}, x = \frac{1}{1 0 ^{3}}

x = 1 0^{3}, x = \frac{1}{1 0 ^{3}}

Verify Solutions:

x = 1 0^{3}

True

, x = \frac{1}{1 0 ^{3}}

True

The solutions are

x = 1 0^{3}, x = \frac{1}{1 0 ^{3}}

10 e^{3 x} = 4^{x}

2^{3 x + 1} = 4^{x}

3^{2 x - 1} = 243

4 9^{x} - 7^{x + 1} + 10 = 0

5^{7 x - 4} = 125

What is the answer to x^{log_{10}(x)}=1000 ?
The answer to x^{log_{10}(x)}=1000 is x=10^{sqrt(3)},x= 1/(10^{sqrt(3))}
Solve for x: x^{log_{10}(x)}=1000
The solution is x=10^{sqrt(3)},x= 1/(10^{sqrt(3))}