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

The answer to ln(x)+ln(x-1)=5 is x=(1+sqrt(1+4e^5))/2

Solve for x: ln(x)+ln(x-1)=5

The solution is x=(1+sqrt(1+4e^5))/2

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

x = \frac{1 + 1 + 4 e ^{5}}{2}

Decimal

x = 12.69275 \dots

Solution steps

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

Apply log rules

x (x - 1) = e^{5}

Solve

x (x - 1) = e^{5} : x = \frac{1 + 1 + 4 e ^{5}}{2}, x = \frac{1 - 1 + 4 e ^{5}}{2}

x = \frac{1 + 1 + 4 e ^{5}}{2}, x = \frac{1 - 1 + 4 e ^{5}}{2}

Verify Solutions:

x = \frac{1 + 1 + 4 e ^{5}}{2}

True

, x = \frac{1 - 1 + 4 e ^{5}}{2}

False

The solution is

x = \frac{1 + 1 + 4 e ^{5}}{2}

3 lo g_{10} (10 x) = - 6

lo g_{125} (x) = - \frac{2}{3}

lo g_{2} (7 x) = 3

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

20 lo g_{10} (\frac{x}{1}) = a

What is the answer to ln(x)+ln(x-1)=5 ?
The answer to ln(x)+ln(x-1)=5 is x=(1+sqrt(1+4e^5))/2
Solve for x: ln(x)+ln(x-1)=5
The solution is x=(1+sqrt(1+4e^5))/2