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

The answer to log_{2}(x+5)=5-log_{2}(x) is x=(-5+3sqrt(17))/2

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

The solution is x=(-5+3sqrt(17))/2

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

x = \frac{- 5 + 3 17}{2}

Solution steps

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

Add

lo g_{2} (x)

to both sides

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

Simplify

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

Apply log rules

(x + 5) x = 32

Solve

(x + 5) x = 32 : x = \frac{- 5 + 3 17}{2}, x = \frac{- 5 - 3 17}{2}

x = \frac{- 5 + 3 17}{2}, x = \frac{- 5 - 3 17}{2}

Verify Solutions:

x = \frac{- 5 + 3 17}{2}

True

, x = \frac{- 5 - 3 17}{2}

False

The solution is

x = \frac{- 5 + 3 17}{2}

x, f x = lo g_{10} (x - 3)

lo g_{10} (6 - 2 x) = 1 + lo g_{10} (x)

y, x = 2 lo g_{10} (y)

lo g_{10} (p^{- 1}) = 1

lo g_{3} (x) + 3 = 2

What is the answer to log_{2}(x+5)=5-log_{2}(x) ?
The answer to log_{2}(x+5)=5-log_{2}(x) is x=(-5+3sqrt(17))/2
Solve for x: log_{2}(x+5)=5-log_{2}(x)
The solution is x=(-5+3sqrt(17))/2