What are the solutions to the equation log_{10}(2)(x^2-4)-log_{10}(2)(2x+4)=4 ?

The solutions to the equation log_{10}(2)(x^2-4)-log_{10}(2)(2x+4)=4 are

Find the zeros of log_{10}(2)(x^2-4)-log_{10}(2)(2x+4)=4

The zeros of log_{10}(2)(x^2-4)-log_{10}(2)(2x+4)=4 are

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lo g_{10} (2) (x^{2} - 4) - lo g_{10} (2) (2 x + 4) = 4

x = \frac{2 lo g _{10} ( 2 ) + 36 lo g _{10} ( 2 ) ^{2} + 16 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}, x = \frac{2 lo g _{10} ( 2 ) - 36 lo g _{10} ( 2 ) ^{2} + 16 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

Decimal Notation

x = 5.72098 \dots, x = - 3.72098 \dots

Solution steps

lo g_{10} (2) (x^{2} - 4) - lo g_{10} (2) (2 x + 4) = 4

Expand

lo g_{10} (2) (x^{2} - 4) - lo g_{10} (2) (2 x + 4) : lo g_{10} (2) x^{2} - 2 lo g_{10} (2) x - 8 lo g_{10} (2)

lo g_{10} (2) x^{2} - 2 lo g_{10} (2) x - 8 lo g_{10} (2) = 4

Move

4

to the left side

lo g_{10} (2) x^{2} - 2 lo g_{10} (2) x - 8 lo g_{10} (2) - 4 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 lo g _{10} ( 2 ) ) \pm ( - 2 lo g _{10} ( 2 ) ) ^{2} - 4 lo g _{10} ( 2 ) ( - 8 lo g _{10} ( 2 ) - 4 )}{2 lo g _{10} ( 2 )}

(- 2 lo g_{10} (2))^{2} - 4 lo g_{10} (2) (- 8 lo g_{10} (2) - 4) = 36 lo g_{10} (2)^{2} + 16 lo g_{10} (2)

x_{1, 2} = \frac{- ( - 2 lo g _{10} ( 2 ) ) \pm 36 lo g _{10} ( 2 ) ^{2} + 16 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

Separate the solutions

x_{1} = \frac{- ( - 2 lo g _{10} ( 2 ) ) + 36 lo g _{10} ( 2 ) ^{2} + 16 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}, x_{2} = \frac{- ( - 2 lo g _{10} ( 2 ) ) - 36 lo g _{10} ( 2 ) ^{2} + 16 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

x = \frac{- ( - 2 lo g _{10} ( 2 ) ) + 36 lo g _{10} ( 2 ) ^{2} + 16 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )} : \frac{2 lo g _{10} ( 2 ) + 36 lo g _{10} ( 2 ) ^{2} + 16 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

x = \frac{- ( - 2 lo g _{10} ( 2 ) ) - 36 lo g _{10} ( 2 ) ^{2} + 16 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )} : \frac{2 lo g _{10} ( 2 ) - 36 lo g _{10} ( 2 ) ^{2} + 16 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

The solutions to the quadratic equation are:

x = \frac{2 lo g _{10} ( 2 ) + 36 lo g _{10} ( 2 ) ^{2} + 16 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}, x = \frac{2 lo g _{10} ( 2 ) - 36 lo g _{10} ( 2 ) ^{2} + 16 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

- x^{2} + 6 x - 1

1 - y^{2} = 0

x, 16 x^{2} - 25 = 0

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

11 x^{2} - 4 x = - 2

What are the solutions to the equation log_{10}(2)(x^2-4)-log_{10}(2)(2x+4)=4 ?
The solutions to the equation log_{10}(2)(x^2-4)-log_{10}(2)(2x+4)=4 are
Find the zeros of log_{10}(2)(x^2-4)-log_{10}(2)(2x+4)=4
The zeros of log_{10}(2)(x^2-4)-log_{10}(2)(2x+4)=4 are