What is the answer to ln(x+13)-ln(x)=2 ?

The answer to ln(x+13)-ln(x)=2 is x=(13)/(e^2-1)

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ln(x+13)-ln(x)=2

ln (x + 13) - ln (x) = 2

x = \frac{13}{e ^{2} - 1}

Decimal

x = 2.03472 \dots

Solution steps

ln (x + 13) - ln (x) = 2

Add

ln (x)

to both sides

ln (x + 13) - ln (x) + ln (x) = 2 + ln (x)

Simplify

ln (x + 13) = 2 + ln (x)

Apply log rules

x + 13 = e^{2} x

Solve

x + 13 = e^{2} x : x = \frac{13}{e ^{2} - 1}

x = \frac{13}{e ^{2} - 1}

Verify Solutions:

x = \frac{13}{e ^{2} - 1}

True

The solution is

x = \frac{13}{e ^{2} - 1}

lo g_{x} (32) = - 5

ln (x) - ln (x + 2) = 8

ln (5 x) + 4 = 7

lo g_{4} (x + 3) = \frac{3}{2}

lo g_{3} (9 + x) = 4

What is the answer to ln(x+13)-ln(x)=2 ?
The answer to ln(x+13)-ln(x)=2 is x=(13)/(e^2-1)
Solve for x: ln(x+13)-ln(x)=2
The solution is x=(13)/(e^2-1)