What is the answer to log_{2}(x-2)+log_{2}(x+5)=1 ?

The answer to log_{2}(x-2)+log_{2}(x+5)=1 is x=(-3+sqrt(57))/2

Solve for x: log_{2}(x-2)+log_{2}(x+5)=1

The solution is x=(-3+sqrt(57))/2

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

x = \frac{- 3 + 57}{2}

Decimal Notation

x = 2.27491 \dots

Solution steps

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

Apply log rules

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

Solve

(x - 2) (x + 5) = 2 : x = \frac{- 3 + 57}{2}, x = \frac{- 3 - 57}{2}

x = \frac{- 3 + 57}{2}, x = \frac{- 3 - 57}{2}

Verify Solutions:

x = \frac{- 3 + 57}{2}

True

, x = \frac{- 3 - 57}{2}

False

The solution is

x = \frac{- 3 + 57}{2}

lo g_{x} (2^{x}) = \frac{x}{4}

ln (a) = ln (3 e^{2}) - 2

lo g_{6} (x - 5) + lo g_{6} (x) = 2

lo g_{6} (x - 1) + lo g_{6} (x) = 1

a = - lo g_{10} (x)

What is the answer to log_{2}(x-2)+log_{2}(x+5)=1 ?
The answer to log_{2}(x-2)+log_{2}(x+5)=1 is x=(-3+sqrt(57))/2
Solve for x: log_{2}(x-2)+log_{2}(x+5)=1
The solution is x=(-3+sqrt(57))/2