What is the answer to |ln(x+3)|=1 ?

The answer to |ln(x+3)|=1 is x= 1/e-3,x=e-3

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|ln(x+3)|=1

∣ ln (x + 3) ∣ = 1

x = \frac{1}{e} - 3, x = e - 3

Decimal Notation

x = - 2.63212 \dots, x = - 0.28171 \dots

Solution steps

∣ ln (x + 3) ∣ = 1

Rewrite the equation with

ln (x + 3) = u

∣ u ∣ = 1

Solve

∣ u ∣ = 1 : u = - 1 or u = 1

u = - 1, u = 1

Substitute back

u = ln (x + 3),

solve for

x

Solve

ln (x + 3) = - 1 : x = \frac{1}{e} - 3

Solve

ln (x + 3) = 1 : x = e - 3

x = \frac{1}{e} - 3, x = e - 3

Verify Solutions:

x = \frac{1}{e} - 3

True

, x = e - 3

True

The solutions are

x = \frac{1}{e} - 3, x = e - 3

lo g_{3} (4) + lo g_{3} (x) = 1

7.4 = lo g_{10} (x)

y, ln (y) = e^{x} + ln (x)

lo g_{4} (8 x + 1) = 2

lo g_{a} (n^{m}) = 16