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

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

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

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

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

Decimal Notation

x = 0.15651 \dots

Solution steps

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

Add

ln (x)

to both sides

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

Simplify

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

Apply log rules

x + 1 = e^{2} x

Solve

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

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

Verify Solutions:

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

True

The solution is

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

2 + lo g_{2} (x) = 15 lo g_{x} (2)

ln (\frac{10}{7 - 2 x}) = ln (2 x)

lo g_{4} (x) = - 3

lo g_{\frac{1}{2}} (x) = - 3

e^{l n (x)} = x

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