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

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

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

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

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

Decimal Notation

x = 10, x = 0.1

Solution steps

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

Apply log rules

(1 + lo g_{10} (x)) lo g_{10} (x) = lo g_{10} (x) + 1

Rewrite the equation with

lo g_{10} (x) = u

(1 + u) u = u + 1

Solve

(1 + u) u = u + 1 : u = 1, u = - 1

u = 1, u = - 1

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

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

Solve

lo g_{10} (x) = - 1 : 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}

(lo g_{10} (x))^{2} = lo g_{10} (x^{2})

2 lo g_{10} (x) - lo g_{10} (x + 6) = 0

ln (\frac{1}{x}) + ln (2 x^{3}) = ln^{3} (x)

2 lo g_{10} (x) + 1 = lo g_{250} (x)

lo g_{10} (x) - 4 (\frac{1 - x}{2}) = 1

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