What is the answer to -ln^3(x)+ln(x)+2=0 ?

The answer to -ln^3(x)+ln(x)+2=0 is x=4.57853…

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-ln^3(x)+ln(x)+2=0

- ln^{3} (x) + ln (x) + 2 = 0

x = 4.57853 \dots

Solution steps

- ln^{3} (x) + ln (x) + 2 = 0

Rewrite the equation with

ln (x) = u

- u^{3} + u + 2 = 0

Solve

- u^{3} + u + 2 = 0 : u \approx 1.52137 \dots

u \approx 1.52137 \dots

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 1.52137 \dots : x = 4.57853 \dots

x = 4.57853 \dots

Verify Solutions:

x = 4.57853 \dots

True

The solution is

x = 4.57853 \dots

y, x = - ln (2 - y)

ln (x) = 15

ln (x) - x = - ln (0.8)

2 lo g_{x} (8) - lo g_{10} (x) 4 = 2

2 lo g_{10} (x) lo g_{10} (x + 6) = 0

What is the answer to -ln^3(x)+ln(x)+2=0 ?
The answer to -ln^3(x)+ln(x)+2=0 is x=4.57853…
Solve for x: -ln^3(x)+ln(x)+2=0
The solution is x=4.57853…