What is the answer to sqrt(ln(x))=ln(sqrt(x)) ?

The answer to sqrt(ln(x))=ln(sqrt(x)) is x=e^4,x=1

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sqrt(ln(x))=ln(sqrt(x))

ln (x) = ln (x)

x = e^{4}, x = 1

Decimal Notation

x = 54.59815 \dots, x = 1

Solution steps

ln (x) = ln (x)

Apply log rules

ln (x) = \frac{1}{2} ln (x)

Rewrite the equation with

ln (x) = u

u = \frac{1}{2} u

Solve

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

u = 4, u = 0

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 4 : x = e^{4}

Solve

ln (x) = 0 : x = 1

x = e^{4}, x = 1

Verify Solutions:

x = e^{4}

True

, x = 1

True

The solutions are

x = e^{4}, x = 1

y, ln (y) = ln (x) + c

lo g_{2} (x - 5) = 2 - lo g_{2} (x - 2)

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

lo g_{10} (x) + lo g_{10} (4) = 0

lo g_{10} (x^{2}) = lo g_{3} (x)

What is the answer to sqrt(ln(x))=ln(sqrt(x)) ?
The answer to sqrt(ln(x))=ln(sqrt(x)) is x=e^4,x=1
Solve for x: sqrt(ln(x))=ln(sqrt(x))
The solution is x=e^4,x=1