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

The answer to ln(x-3)+ln(x-5)=2 is x=(8+sqrt(4e^2+4))/2

Solve for x: ln(x-3)+ln(x-5)=2

The solution is x=(8+sqrt(4e^2+4))/2

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

x = \frac{8 + 4 e ^{2} + 4}{2}

Decimal

x = 6.89638 \dots

Solution steps

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

Apply log rules

(x - 3) (x - 5) = e^{2}

Solve

(x - 3) (x - 5) = e^{2} : x = \frac{8 + 4 e ^{2} + 4}{2}, x = \frac{8 - 4 e ^{2} + 4}{2}

x = \frac{8 + 4 e ^{2} + 4}{2}, x = \frac{8 - 4 e ^{2} + 4}{2}

Verify Solutions:

x = \frac{8 + 4 e ^{2} + 4}{2}

True

, x = \frac{8 - 4 e ^{2} + 4}{2}

False

The solution is

x = \frac{8 + 4 e ^{2} + 4}{2}

ln (x) - ln (3) = 4

lo g_{5} (x + 8) = 3

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

lo g_{10} (x^{3}) = lo g_{10} (6) + 2 lo g_{10} (x)

ln (\frac{x + 1 + e ^{2}}{x + 1}) = 2

What is the answer to ln(x-3)+ln(x-5)=2 ?
The answer to ln(x-3)+ln(x-5)=2 is x=(8+sqrt(4e^2+4))/2
Solve for x: ln(x-3)+ln(x-5)=2
The solution is x=(8+sqrt(4e^2+4))/2