What is the answer to ln(x+1)=ln(5+x)-ln(x+2) ?

The answer to ln(x+1)=ln(5+x)-ln(x+2) is x=1

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ln(x+1)=ln(5+x)-ln(x+2)

ln (x + 1) = ln (5 + x) - ln (x + 2)

x = 1

Solution steps

ln (x + 1) = ln (5 + x) - ln (x + 2)

Add

ln (x + 2)

to both sides

ln (x + 1) + ln (x + 2) = ln (5 + x) - ln (x + 2) + ln (x + 2)

Simplify

ln (x + 1) + ln (x + 2) = ln (5 + x)

Apply log rules

(x + 1) (x + 2) = 5 + x

Solve

(x + 1) (x + 2) = 5 + x : x = 1, x = - 3

x = 1, x = - 3

Verify Solutions:

x = 1

True

, x = - 3

False

The solution is

x = 1

ln (3 - 2 x) - 2 ln (x) = 0

3 = ln (x)

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

0.64 = lo g_{10} (x)

y^{3 l o g_{10} (y)} = 100 y

What is the answer to ln(x+1)=ln(5+x)-ln(x+2) ?
The answer to ln(x+1)=ln(5+x)-ln(x+2) is x=1
Solve for x: ln(x+1)=ln(5+x)-ln(x+2)
The solution is x=1