What is the answer to ln(x+6)-ln(2x-1)=1 ?

The answer to ln(x+6)-ln(2x-1)=1 is x=(e+6)/(2e-1)

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ln(x+6)-ln(2x-1)=1

ln (x + 6) - ln (2 x - 1) = 1

x = \frac{e + 6}{2 e - 1}

Decimal Notation

x = 1.96509 \dots

Solution steps

ln (x + 6) - ln (2 x - 1) = 1

Add

ln (2 x - 1)

to both sides

ln (x + 6) - ln (2 x - 1) + ln (2 x - 1) = 1 + ln (2 x - 1)

Simplify

ln (x + 6) = 1 + ln (2 x - 1)

Apply log rules

x + 6 = e (2 x - 1)

Solve

x + 6 = e (2 x - 1) : x = \frac{e + 6}{2 e - 1}

x = \frac{e + 6}{2 e - 1}

Verify Solutions:

x = \frac{e + 6}{2 e - 1}

True

The solution is

x = \frac{e + 6}{2 e - 1}

lo g_{2} (x - 1) = 0

7.6 = lo g_{10} (\frac{x}{4})

\frac{9}{4} lo g_{5} (x) = - 8

16 t^{2} ln (t) + 8 t^{2} = 0

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

What is the answer to ln(x+6)-ln(2x-1)=1 ?
The answer to ln(x+6)-ln(2x-1)=1 is x=(e+6)/(2e-1)
Solve for x: ln(x+6)-ln(2x-1)=1
The solution is x=(e+6)/(2e-1)