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

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

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

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

Rewrite the equation with

ln (x) = u

\frac{1}{2} u = u

Solve

\frac{1}{2} u = 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

lo g_{10} (x) = 0.66

ln (x) + ln (x - 5) = 0

lo g_{9} (x) = \frac{3}{2}

ln (x + 9) = 1

ln (x) = 2 + ln (1 - x)

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