What is the answer to (ln(x))^2-1=0 ?

The answer to (ln(x))^2-1=0 is x=e,x= 1/e

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(ln(x))^2-1=0

(ln (x))^{2} - 1 = 0

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

Decimal Notation

x = 2.71828 \dots, x = 0.36787 \dots

Solution steps

(ln (x))^{2} - 1 = 0

Rewrite the equation with

ln (x) = u

(u)^{2} - 1 = 0

Solve

u^{2} - 1 = 0 : u = 1, u = - 1

u = 1, u = - 1

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 1 : x = e

Solve

ln (x) = - 1 : x = \frac{1}{e}

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

Verify Solutions:

x = e

True

, x = \frac{1}{e}

True

The solutions are

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

lo g_{x} (\frac{25}{9}) = 2

ln (2 - x) = 3

ln (x) = ln (5)

ln (x) = ln (6)

lo g_{x} (1024) = x