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

The answer to ln(2x+1)-ln(x)=2ln(3) is x= 1/7

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

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

x = \frac{1}{7}

Decimal Notation

x = 0.14285 \dots

Solution steps

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

Add

ln (x)

to both sides

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

Simplify

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

Apply log rules

2 x + 1 = 9 x

Solve

2 x + 1 = 9 x : x = \frac{1}{7}

x = \frac{1}{7}

Verify Solutions:

x = \frac{1}{7}

True

The solution is

x = \frac{1}{7}

lo g_{10} (25) = 2 lo g_{10} (x)

3 lo g_{2} (3 x + 1) = 6

(ln (x))^{2} = 4

(ln (x))^{2} = 1

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

What is the answer to ln(2x+1)-ln(x)=2ln(3) ?
The answer to ln(2x+1)-ln(x)=2ln(3) is x= 1/7
Solve for x: ln(2x+1)-ln(x)=2ln(3)
The solution is x= 1/7