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

The answer to sqrt(log_{10)(x)}=log_{10}(sqrt(x)) is x=10000,x=1

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sqrt(log_{10)(x)}=log_{10}(sqrt(x))

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

x = 10000, x = 1

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{10} (x) = u

u = \frac{1}{2} u

Solve

u = \frac{1}{2} u : u = 4, u = 0

u = 4, u = 0

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 4 : x = 10000

Solve

lo g_{10} (x) = 0 : x = 1

x = 10000, x = 1

Verify Solutions:

x = 10000

True

, x = 1

True

The solutions are

x = 10000, x = 1

lo g_{0.1} (x^{2} + 3 x) = - 1

3 x^{2} ln (x) + x^{2} = 0

lo g_{3} (x) + 1 = 0

lo g_{3} (2 x) - lo g_{3} (x + 5) = 0

2 ln (x) - ln (3) = 0

What is the answer to sqrt(log_{10)(x)}=log_{10}(sqrt(x)) ?
The answer to sqrt(log_{10)(x)}=log_{10}(sqrt(x)) is x=10000,x=1
Solve for x: sqrt(log_{10)(x)}=log_{10}(sqrt(x))
The solution is x=10000,x=1