What is the answer to (ln(x))^2=10-9ln(x) ?

The answer to (ln(x))^2=10-9ln(x) is x=e,x= 1/(e^{10)}

Solve for x: (ln(x))^2=10-9ln(x)

The solution is x=e,x= 1/(e^{10)}

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(ln (x))^{2} = 10 - 9 ln (x)

x = e, x = \frac{1}{e ^{10}}

Decimal Notation

x = 2.71828 \dots, x = 0.00004 \dots

Solution steps

(ln (x))^{2} = 10 - 9 ln (x)

Rewrite the equation with

ln (x) = u

(u)^{2} = 10 - 9 u

Solve

u^{2} = 10 - 9 u : u = 1, u = - 10

u = 1, u = - 10

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 1 : x = e

Solve

ln (x) = - 10 : x = \frac{1}{e ^{10}}

x = e, x = \frac{1}{e ^{10}}

Verify Solutions:

x = e

True

, x = \frac{1}{e ^{10}}

True

The solutions are

x = e, x = \frac{1}{e ^{10}}

ln (x + 9) + ln (x - 5) = 2 ln (x)

x ln (x) = 6 ln (x)

\frac{4 ln ( x )}{x} = 5

lo g_{2} ((r + 4)^{2}) = 6

ln (x) + 2 x - 2 = 0

What is the answer to (ln(x))^2=10-9ln(x) ?
The answer to (ln(x))^2=10-9ln(x) is x=e,x= 1/(e^{10)}
Solve for x: (ln(x))^2=10-9ln(x)
The solution is x=e,x= 1/(e^{10)}