What is the answer to ln(x)+ln(x-10)=3 ?

The answer to ln(x)+ln(x-10)=3 is x=(10+sqrt(100+4e^3))/2

Solve for x: ln(x)+ln(x-10)=3

The solution is x=(10+sqrt(100+4e^3))/2

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ln (x) + ln (x - 10) = 3

x = \frac{10 + 100 + 4 e ^{3}}{2}

Decimal Notation

x = 11.71457 \dots

Solution steps

ln (x) + ln (x - 10) = 3

Apply log rules

x (x - 10) = e^{3}

Solve

x (x - 10) = e^{3} : x = \frac{10 + 100 + 4 e ^{3}}{2}, x = \frac{10 - 100 + 4 e ^{3}}{2}

x = \frac{10 + 100 + 4 e ^{3}}{2}, x = \frac{10 - 100 + 4 e ^{3}}{2}

Verify Solutions:

x = \frac{10 + 100 + 4 e ^{3}}{2}

True

, x = \frac{10 - 100 + 4 e ^{3}}{2}

False

The solution is

x = \frac{10 + 100 + 4 e ^{3}}{2}

ln (x) + ln (x - 10) = 1

lo g_{10} (2 x + 4) = 2, x

- ln (x) + 2 = 0

2 + lo g_{3} (2 x + 5) - lo g_{3} (x) = 4

lo g_{2} (5 - 2 x) = 3 + lo g_{2} (x + 1)

What is the answer to ln(x)+ln(x-10)=3 ?
The answer to ln(x)+ln(x-10)=3 is x=(10+sqrt(100+4e^3))/2
Solve for x: ln(x)+ln(x-10)=3
The solution is x=(10+sqrt(100+4e^3))/2