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

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

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ln(x)=ln(2x-1)-ln(x-2)

ln (x) = ln (2 x - 1) - ln (x - 2)

x = 2 + 3

Decimal Notation

x = 3.73205 \dots

Solution steps

ln (x) = ln (2 x - 1) - ln (x - 2)

Add

ln (x - 2)

to both sides

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

Simplify

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

Apply log rules

x (x - 2) = 2 x - 1

Solve

x (x - 2) = 2 x - 1 : x = 2 + 3, x = 2 - 3

x = 2 + 3, x = 2 - 3

Verify Solutions:

x = 2 + 3

True

, x = 2 - 3

False

The solution is

x = 2 + 3

- 3 lo g_{7} (- 5 n - 7) = 0

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

1 + lo g_{6} (x) = lo g_{6} (2 x + 4)

x, lo g_{2} (x) = 4

6.01 - 9.69 = lo g_{10} (x)

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