What is the answer to ln(x+6)-ln(x-3)=1 ?

The answer to ln(x+6)-ln(x-3)=1 is x=(3e+6)/(e-1)

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ln(x+6)-ln(x-3)=1

ln (x + 6) - ln (x - 3) = 1

x = \frac{3 e + 6}{e - 1}

Decimal Notation

x = 8.23779 \dots

Solution steps

ln (x + 6) - ln (x - 3) = 1

Add

ln (x - 3)

to both sides

ln (x + 6) - ln (x - 3) + ln (x - 3) = 1 + ln (x - 3)

Simplify

ln (x + 6) = 1 + ln (x - 3)

Apply log rules

x + 6 = e (x - 3)

Solve

x + 6 = e (x - 3) : x = \frac{3 e + 6}{e - 1}

x = \frac{3 e + 6}{e - 1}

Verify Solutions:

x = \frac{3 e + 6}{e - 1}

True

The solution is

x = \frac{3 e + 6}{e - 1}

lo g_{3} (4 x - 1) - 2 lo g_{3} (x) = 1

lo g_{3} (x + 3) + lo g_{3} (4 x + 7) = 2

y, x = ln (2 y + 1)

ln (x + 9) - ln (x + 7) = 3

lo g_{10} (x + 1) = lo g_{10} (x) + 1

What is the answer to ln(x+6)-ln(x-3)=1 ?
The answer to ln(x+6)-ln(x-3)=1 is x=(3e+6)/(e-1)
Solve for x: ln(x+6)-ln(x-3)=1
The solution is x=(3e+6)/(e-1)