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Question

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

1. Solve equation by setting up algebraically.
2. Use appropriate properties of Logarithm to reduce the number of logarithmic terms to only one.
3. Solve logarithmic equation.

Answer 1

ln(x + 1) - ln(x + 2) = ln5,

2. ln((x + 1) / (x + 2))) = ln5.

3. ln((x + 1) / (x + 2)) = 1.6094,
(x + 1) / (x + 2) = e^1.6094,
(x + 1) / (x + 2) = 5,
Cross multiply:
5X + 10 = X + 1,
5X - X = 1 - 10,
4X = - 9,
X = -2 1/4 = -9/4.

Answer 2

CORRECTION:I copied the problem wrong.

ln(x + 1) - ln(x - 2) = ln5.

2. ln((x + 1) / (x - 2)) = ln5.

3. ln((x + 1) / (x - 2)) = 1.6094,
(x + 1) / (x - 2) = e^1.6094,
(x + 1) / (x - 2) = 5,
Cross multiply:
5X - 10 = X + 1,
5X - X = 1 + 10,
4X = 11,
X = 2 3/4 = 11/4.

Answer 3

3lnx+2lny-4lnz