What is the answer to ln(x+2)-ln(6-x)=ln(x-1) ?

The answer to ln(x+2)-ln(6-x)=ln(x-1) is x=2,x=4

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ln(x+2)-ln(6-x)=ln(x-1)

ln (x + 2) - ln (6 - x) = ln (x - 1)

x = 2, x = 4

Solution steps

ln (x + 2) - ln (6 - x) = ln (x - 1)

Add

ln (6 - x)

to both sides

ln (x + 2) - ln (6 - x) + ln (6 - x) = ln (x - 1) + ln (6 - x)

Simplify

ln (x + 2) = ln (x - 1) + ln (6 - x)

Apply log rules

x + 2 = (x - 1) (6 - x)

Solve

x + 2 = (x - 1) (6 - x) : x = 2, x = 4

x = 2, x = 4

Verify Solutions:

x = 2

True

, x = 4

True

The solutions are

x = 2, x = 4

lo g_{2} (x^{9}) = - 9

lo g_{4 x} (2 x + 5) = \frac{8}{5}

- 9 lo g_{2} (8 - 9 x) - 5 = - 41

lo g_{5} (x^{2} - 24 x) = 2

lo g_{10} (x) = - 0.26916

What is the answer to ln(x+2)-ln(6-x)=ln(x-1) ?
The answer to ln(x+2)-ln(6-x)=ln(x-1) is x=2,x=4
Solve for x: ln(x+2)-ln(6-x)=ln(x-1)
The solution is x=2,x=4