What is the answer to ln(x-1)+ln(x-2)=ln|4-x| ?

The answer to ln(x-1)+ln(x-2)=ln|4-x| is x=1+sqrt(3)

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ln(x-1)+ln(x-2)=ln|4-x|

ln (x - 1) + ln (x - 2) = ln ∣ 4 - x ∣

x = 1 + 3

Decimal Notation

x = 2.73205 \dots

Solution steps

ln (x - 1) + ln (x - 2) = ln ∣ 4 - x ∣

Apply log rules

(x - 1) (x - 2) = ∣ 4 - x ∣

Solve

(x - 1) (x - 2) = ∣ 4 - x ∣ : x = 1 - 3 or x = 1 + 3

x = 1 - 3 or x = 1 + 3

Verify Solutions:

x = 1 - 3

False

, x = 1 + 3

True

The solution is

x = 1 + 3

\frac{1}{2} \cdot 16

(x + 2)^{2} - (x + 2) - 42

x^{2} + 18 x + 74 = 0

- 5 x^{2} + 88 x = 0

12 k^{2} - k - 20

What is the answer to ln(x-1)+ln(x-2)=ln|4-x| ?
The answer to ln(x-1)+ln(x-2)=ln|4-x| is x=1+sqrt(3)
Solve for x: ln(x-1)+ln(x-2)=ln|4-x|
The solution is x=1+sqrt(3)