What is the answer to ln(x)+ln(x+8)=3 ?

The answer to ln(x)+ln(x+8)=3 is x=(-8+sqrt(64+4e^3))/2

Solve for x: ln(x)+ln(x+8)=3

The solution is x=(-8+sqrt(64+4e^3))/2

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ln (x) + ln (x + 8) = 3

x = \frac{- 8 + 64 + 4 e ^{3}}{2}

Decimal

x = 2.00712 \dots

Solution steps

ln (x) + ln (x + 8) = 3

Apply log rules

x (x + 8) = e^{3}

Solve

x (x + 8) = e^{3} : x = \frac{- 8 + 64 + 4 e ^{3}}{2}, x = \frac{- 8 - 64 + 4 e ^{3}}{2}

x = \frac{- 8 + 64 + 4 e ^{3}}{2}, x = \frac{- 8 - 64 + 4 e ^{3}}{2}

Verify Solutions:

x = \frac{- 8 + 64 + 4 e ^{3}}{2}

True

, x = \frac{- 8 - 64 + 4 e ^{3}}{2}

False

The solution is

x = \frac{- 8 + 64 + 4 e ^{3}}{2}

lo g_{10} (N + M)

lo g_{10} (7) = \frac{3}{4} lo g_{10} (49) - lo g_{10} (x)

lo g_{x} (\frac{1}{1296}) = 4

lo g_{x} (729) = \frac{3}{2}

lo g_{10} (x) = - \frac{5}{7}

What is the answer to ln(x)+ln(x+8)=3 ?
The answer to ln(x)+ln(x+8)=3 is x=(-8+sqrt(64+4e^3))/2
Solve for x: ln(x)+ln(x+8)=3
The solution is x=(-8+sqrt(64+4e^3))/2