What is the answer to ln(x+1)-ln(x-5)=3 ?

The answer to ln(x+1)-ln(x-5)=3 is x=(5e^3+1)/(e^3-1)

Solve for x: ln(x+1)-ln(x-5)=3

The solution is x=(5e^3+1)/(e^3-1)

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ln (x + 1) - ln (x - 5) = 3

x = \frac{5 e ^{3} + 1}{e ^{3} - 1}

Decimal Notation

x = 5.31437 \dots

Solution steps

ln (x + 1) - ln (x - 5) = 3

Add

ln (x - 5)

to both sides

ln (x + 1) - ln (x - 5) + ln (x - 5) = 3 + ln (x - 5)

Simplify

ln (x + 1) = 3 + ln (x - 5)

Apply log rules

x + 1 = e^{3} (x - 5)

Solve

x + 1 = e^{3} (x - 5) : x = \frac{5 e ^{3} + 1}{e ^{3} - 1}

x = \frac{5 e ^{3} + 1}{e ^{3} - 1}

Verify Solutions:

x = \frac{5 e ^{3} + 1}{e ^{3} - 1}

True

The solution is

x = \frac{5 e ^{3} + 1}{e ^{3} - 1}

0 = - \frac{ln ( - 3 ( 0 ) ^{2} + c )}{2}

lo g_{5} (2 (x^{3} + 5)) = 2

lo g_{- x - 1} (2 x^{2} - x + 1) = 2

lo g_{9} (2 x - 5) = 0.5

lo g_{9} (27 x) + lo g_{x} (81) = 6

What is the answer to ln(x+1)-ln(x-5)=3 ?
The answer to ln(x+1)-ln(x-5)=3 is x=(5e^3+1)/(e^3-1)
Solve for x: ln(x+1)-ln(x-5)=3
The solution is x=(5e^3+1)/(e^3-1)