What is the answer to ln(ln(x^2))=2ln(ln(x)) ?

The answer to ln(ln(x^2))=2ln(ln(x)) is x=e^2

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ln(ln(x^2))=2ln(ln(x))

ln (ln (x^{2})) = 2 ln (ln (x))

x = e^{2}

Decimal Notation

x = 7.38905 \dots

Solution steps

ln (ln (x^{2})) = 2 ln (ln (x))

Apply log rules

2 ln (x) = ln^{2} (x)

Rewrite the equation with

ln (x) = u

2 u = u^{2}

Solve

2 u = u^{2} : u = 2, u = 0

u = 2, u = 0

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 2 : x = e^{2}

Solve

ln (x) = 0 : x = 1

x = e^{2}, x = 1

Verify Solutions:

x = e^{2}

True

, x = 1

False

The solution is

x = e^{2}

lo g_{x} (6) = 7

0 = 1.88 + (- 0.225) ln (x)

ln (3 x) - 2 = 5

b, lo g_{b} (9) = 2

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

What is the answer to ln(ln(x^2))=2ln(ln(x)) ?
The answer to ln(ln(x^2))=2ln(ln(x)) is x=e^2
Solve for x: ln(ln(x^2))=2ln(ln(x))
The solution is x=e^2