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

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

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ln(x)=ln^2(x)

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

x = e, x = 1

Solution steps

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

Rewrite the equation with

ln (x) = u

u = u^{2}

Solve

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

u = 1, u = 0

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 1 : x = e

Solve

ln (x) = 0 : x = 1

x = e, x = 1

Verify Solutions:

x = e

True

, x = 1

True

The solutions are

x = e, x = 1

lo g_{6} (5 x) = 3

lo g_{10} (x) + lo g_{10} (x + 90) = 3

t, ln (2 t + 3) = 4

1 = 2.22 + lo g_{10} (x)

lo g_{2} (8 x - 3) = 2 + lo g_{10} (2)