What is the answer to ln(5x)-ln(3-2x)=1 ?

The answer to ln(5x)-ln(3-2x)=1 is x=(3e)/(5+2e)

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ln(5x)-ln(3-2x)=1

ln (5 x) - ln (3 - 2 x) = 1

x = \frac{3 e}{5 + 2 e}

Decimal Notation

x = 0.78137 \dots

Solution steps

ln (5 x) - ln (3 - 2 x) = 1

Add

ln (3 - 2 x)

to both sides

ln (5 x) - ln (3 - 2 x) + ln (3 - 2 x) = 1 + ln (3 - 2 x)

Simplify

ln (5 x) = 1 + ln (3 - 2 x)

Apply log rules

5 x = e (3 - 2 x)

Solve

5 x = e (3 - 2 x) : x = \frac{3 e}{5 + 2 e}

x = \frac{3 e}{5 + 2 e}

Verify Solutions:

x = \frac{3 e}{5 + 2 e}

True

The solution is

x = \frac{3 e}{5 + 2 e}

2 ln (x) + 1 = 0

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

lo g_{3} (y) + 4 lo g_{y} (3) = 4

lo g_{\frac{1}{2}} (x) = - 1

lo g_{10} (4 x) + lo g_{10} (8 x) = 1

What is the answer to ln(5x)-ln(3-2x)=1 ?
The answer to ln(5x)-ln(3-2x)=1 is x=(3e)/(5+2e)
Solve for x: ln(5x)-ln(3-2x)=1
The solution is x=(3e)/(5+2e)