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

The answer to ln((x-2)^2)-ln(x)=0 is x=4,x=1

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

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

x = 4, x = 1

Solution steps

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

Add

ln (x)

to both sides

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

Simplify

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

Apply log rules

(x - 2)^{2} = x

Solve

(x - 2)^{2} = x : x = 4, x = 1

x = 4, x = 1

Verify Solutions:

x = 4

True

, x = 1

True

The solutions are

x = 4, x = 1

3 = lo g_{10} (x)

lo g_{10} (2 x) - lo g_{10} (x - 3) = 1

ln (2 x) = 4

ln (x - 3) + ln (x - 2) = ln (2 x + 24)

lo g_{10} (5 x) = 2

What is the answer to ln((x-2)^2)-ln(x)=0 ?
The answer to ln((x-2)^2)-ln(x)=0 is x=4,x=1
Solve for x: ln((x-2)^2)-ln(x)=0
The solution is x=4,x=1