What is the answer to ln(x+3)+ln(x)-ln(2x)=3 ?

The answer to ln(x+3)+ln(x)-ln(2x)=3 is x=-3+2e^3

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ln(x+3)+ln(x)-ln(2x)=3

ln (x + 3) + ln (x) - ln (2 x) = 3

x = - 3 + 2 e^{3}

Decimal Notation

x = 37.17107 \dots

Solution steps

ln (x + 3) + ln (x) - ln (2 x) = 3

Apply log rules

(x + 3) x = e^{3} \cdot 2 x

Solve

(x + 3) x = e^{3} \cdot 2 x : x = 0, x = - 3 + 2 e^{3}

x = 0, x = - 3 + 2 e^{3}

Verify Solutions:

x = 0

False

, x = - 3 + 2 e^{3}

True

The solution is

x = - 3 + 2 e^{3}

lo g_{6} (9 x) - lo g_{6} (4) = 2

lo g_{10} (x) = - x + 40

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

lo g_{3} (5 x - 7) = 0

0 = 5 (ln (4 x) + 1)

What is the answer to ln(x+3)+ln(x)-ln(2x)=3 ?
The answer to ln(x+3)+ln(x)-ln(2x)=3 is x=-3+2e^3
Solve for x: ln(x+3)+ln(x)-ln(2x)=3
The solution is x=-3+2e^3