What is the answer to ln(x)+3= 4/(ln(x)) ?

The answer to ln(x)+3= 4/(ln(x)) is x=e,x= 1/(e^4)

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ln(x)+3= 4/(ln(x))

ln (x) + 3 = \frac{4}{ln ( x )}

x = e, x = \frac{1}{e ^{4}}

Decimal Notation

x = 2.71828 \dots, x = 0.01831 \dots

Solution steps

ln (x) + 3 = \frac{4}{ln ( x )}

Multiply both sides by

ln (x)

ln (x) ln (x) + 3 ln (x) = \frac{4}{ln ( x )} ln (x)

Simplify

ln (x) ln (x) + 3 ln (x) : ln^{2} (x) + 3 ln (x)

ln^{2} (x) + 3 ln (x) = 4

Rewrite the equation with

ln (x) = u

u^{2} + 3 u = 4

Solve

u^{2} + 3 u = 4 : u = 1, u = - 4

u = 1, u = - 4

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 1 : x = e

Solve

ln (x) = - 4 : x = \frac{1}{e ^{4}}

x = e, x = \frac{1}{e ^{4}}

Verify Solutions:

x = e

True

, x = \frac{1}{e ^{4}}

True

The solutions are

x = e, x = \frac{1}{e ^{4}}

lo g_{7} (9 - x) = 3 lo g_{7} (2)

x, lo g_{10} (x) = - 2

lo g_{10} (x) = 97261

ln (x - 2) = ln (12) - ln (x + 2)

(lo g_{e} (x - 1))^{2} = 4

What is the answer to ln(x)+3= 4/(ln(x)) ?
The answer to ln(x)+3= 4/(ln(x)) is x=e,x= 1/(e^4)
Solve for x: ln(x)+3= 4/(ln(x))
The solution is x=e,x= 1/(e^4)