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

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

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

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

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

Decimal

x = 0.31303 \dots

Solution steps

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

Add

ln (x)

to both sides

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

Simplify

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

Apply log rules

x + 2 = e^{2} x

Solve

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

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

Verify Solutions:

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

True

The solution is

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

lo g_{9} (7 - 2 x) = 2

ln (9) + ln (x + 3) = 3

lo g_{5} (4 x + 11) = 2

- 4 x ln (x) = 0

20 lo g_{10} (x) = 12

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