What is the answer to log_{2}(4X+5)=8-log_{2}(X+1) ?

The answer to log_{2}(4X+5)=8-log_{2}(X+1) is X=(-9+sqrt(4097))/8

Solve for X: log_{2}(4X+5)=8-log_{2}(X+1)

The solution is X=(-9+sqrt(4097))/8

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lo g_{2} (4 X + 5) = 8 - lo g_{2} (X + 1)

X = \frac{- 9 + 4097}{8}

Decimal Notation

X = 6.87597 \dots

Solution steps

lo g_{2} (4 X + 5) = 8 - lo g_{2} (X + 1)

Add

lo g_{2} (X + 1)

to both sides

lo g_{2} (4 X + 5) + lo g_{2} (X + 1) = 8 - lo g_{2} (X + 1) + lo g_{2} (X + 1)

Simplify

lo g_{2} (4 X + 5) + lo g_{2} (X + 1) = 8

Apply log rules

(4 X + 5) (X + 1) = 256

Solve

(4 X + 5) (X + 1) = 256 : X = \frac{- 9 + 4097}{8}, X = \frac{- 9 - 4097}{8}

X = \frac{- 9 + 4097}{8}, X = \frac{- 9 - 4097}{8}

Verify Solutions:

X = \frac{- 9 + 4097}{8}

True

, X = \frac{- 9 - 4097}{8}

False

The solution is

X = \frac{- 9 + 4097}{8}

2 = lo g_{9} (x)

ln (10 - 2 x^{2}) - ln (5) = ln (2)

ln (4 x) - 4 ln (x^{3}) = ln (7)

lo g_{10} (x) - lo g_{10} (2) = 2

x, y^{2} = ln (x + y)

What is the answer to log_{2}(4X+5)=8-log_{2}(X+1) ?
The answer to log_{2}(4X+5)=8-log_{2}(X+1) is X=(-9+sqrt(4097))/8
Solve for X: log_{2}(4X+5)=8-log_{2}(X+1)
The solution is X=(-9+sqrt(4097))/8