What is the answer to ln(2x+1)-ln(x-1)=4 ?

The answer to ln(2x+1)-ln(x-1)=4 is x=(e^4+1)/(e^4-2)

Solve for x: ln(2x+1)-ln(x-1)=4

The solution is x=(e^4+1)/(e^4-2)

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ln (2 x + 1) - ln (x - 1) = 4

x = \frac{e ^{4} + 1}{e ^{4} - 2}

Decimal Notation

x = 1.05703 \dots

Solution steps

ln (2 x + 1) - ln (x - 1) = 4

Add

ln (x - 1)

to both sides

ln (2 x + 1) - ln (x - 1) + ln (x - 1) = 4 + ln (x - 1)

Simplify

ln (2 x + 1) = 4 + ln (x - 1)

Apply log rules

2 x + 1 = e^{4} (x - 1)

Solve

2 x + 1 = e^{4} (x - 1) : x = \frac{e ^{4} + 1}{e ^{4} - 2}

x = \frac{e ^{4} + 1}{e ^{4} - 2}

Verify Solutions:

x = \frac{e ^{4} + 1}{e ^{4} - 2}

True

The solution is

x = \frac{e ^{4} + 1}{e ^{4} - 2}

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

x, ln (y) = lo g_{10} (x)

y, z - ln (y) = 0

x, ln (y) = 3 ln (x) + c

lo g_{2} (x + 3) = lo g_{2} (7)

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