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

The answer to ln(x+3)-ln(x)=ln(6) is x= 3/5

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

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

x = \frac{3}{5}

Solution steps

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

Add

ln (x)

to both sides

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

Simplify

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

Apply log rules

x + 3 = 6 x

Solve

x + 3 = 6 x : x = \frac{3}{5}

x = \frac{3}{5}

Verify Solutions:

x = \frac{3}{5}

True

The solution is

x = \frac{3}{5}

lo g_{3} (x) = 3 + 2 lo g_{x} (9)

ln (x + 5) + ln (x - 1) = 2

2 lo g_{10} (x) = - 10

lo g_{10} (x) = 0.2293300000000 \dots

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

What is the answer to ln(x+3)-ln(x)=ln(6) ?
The answer to ln(x+3)-ln(x)=ln(6) is x= 3/5
Solve for x: ln(x+3)-ln(x)=ln(6)
The solution is x= 3/5