What is the answer to log_{10}(x^{log_{10}(x)})=1 ?

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

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log_{10}(x^{log_{10}(x)})=1

lo g_{10} (x^{l o g_{10} (x)}) = 1

x = 10, x = \frac{1}{10}

Solution steps

lo g_{10} (x^{l o g_{10} (x)}) = 1

Apply exponent rules

lo g_{10} (e^{l o g_{10} (x) l n (x)}) = 1

Rewrite the equation with

e^{l o g_{10} (x) l n (x)} = u

lo g_{10} (u) = 1

Solve

lo g_{10} (u) = 1 : u = 10

u = 10

Substitute back

u = e^{l o g_{10} (x) l n (x)},

solve for

x

Solve

e^{l o g_{10} (x) l n (x)} = 10 : x = 10, x = \frac{1}{10}

x = 10, x = \frac{1}{10}

Verify Solutions:

x = 10

True

, x = \frac{1}{10}

True

The solutions are

x = 10, x = \frac{1}{10}

e^{7 x} = 10

3^{x} = \frac{1}{5}

3^{x} = \frac{1}{8}

e^{20 \cdot l n (x)} = e^{- 3}

e^{2 x - 3} = 37

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