What is the answer to x^{log_{10}(x)}=100 ?

The answer to x^{log_{10}(x)}=100 is x=10^{sqrt(2)},x= 1/(10^{sqrt(2))}

Solve for x: x^{log_{10}(x)}=100

The solution is x=10^{sqrt(2)},x= 1/(10^{sqrt(2))}

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x^{l o g_{10} (x)} = 100

x = 1 0^{2}, x = \frac{1}{1 0 ^{2}}

Decimal Notation

x = 25.95455 \dots, x = 0.03852 \dots

Solution steps

x^{l o g_{10} (x)} = 100

Apply exponent rules

lo g_{10} (x) ln (x) = ln (100)

Solve

lo g_{10} (x) ln (x) = ln (100) : x = 1 0^{2}, x = \frac{1}{1 0 ^{2}}

x = 1 0^{2}, x = \frac{1}{1 0 ^{2}}

Verify Solutions:

x = 1 0^{2}

True

, x = \frac{1}{1 0 ^{2}}

True

The solutions are

x = 1 0^{2}, x = \frac{1}{1 0 ^{2}}

3^{x} = \frac{1}{729}

a^{2 x - 5} = a^{15}

3^{2 x} + 12 = 39

lo g_{7} (2^{5 x}) = 3

7^{x - 5} = 4 9^{x}

What is the answer to x^{log_{10}(x)}=100 ?
The answer to x^{log_{10}(x)}=100 is x=10^{sqrt(2)},x= 1/(10^{sqrt(2))}
Solve for x: x^{log_{10}(x)}=100
The solution is x=10^{sqrt(2)},x= 1/(10^{sqrt(2))}