What are the solutions to the equation log_{10}(5)(4x^2+4)-log_{10}(5)(x+6)=1 ?

The solutions to the equation log_{10}(5)(4x^2+4)-log_{10}(5)(x+6)=1 are

Find the zeros of log_{10}(5)(4x^2+4)-log_{10}(5)(x+6)=1

The zeros of log_{10}(5)(4x^2+4)-log_{10}(5)(x+6)=1 are

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lo g_{10} (5) (4 x^{2} + 4) - lo g_{10} (5) (x + 6) = 1

x = \frac{lo g _{10} ( 5 ) + 33 lo g _{10} ( 5 ) ^{2} + 16 lo g _{10} ( 5 )}{8 lo g _{10} ( 5 )}, x = \frac{lo g _{10} ( 5 ) - 33 lo g _{10} ( 5 ) ^{2} + 16 lo g _{10} ( 5 )}{8 lo g _{10} ( 5 )}

Decimal Notation

x = 1.05950 \dots, x = - 0.80950 \dots

Solution steps

lo g_{10} (5) (4 x^{2} + 4) - lo g_{10} (5) (x + 6) = 1

Expand

lo g_{10} (5) (4 x^{2} + 4) - lo g_{10} (5) (x + 6) : 4 lo g_{10} (5) x^{2} - lo g_{10} (5) x - 2 lo g_{10} (5)

4 lo g_{10} (5) x^{2} - lo g_{10} (5) x - 2 lo g_{10} (5) = 1

Move

1

to the left side

4 lo g_{10} (5) x^{2} - lo g_{10} (5) x - 2 lo g_{10} (5) - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - lo g _{10} ( 5 ) ) \pm ( - lo g _{10} ( 5 ) ) ^{2} - 4 \cdot 4 lo g _{10} ( 5 ) ( - 2 lo g _{10} ( 5 ) - 1 )}{2 \cdot 4 lo g _{10} ( 5 )}

(- lo g_{10} (5))^{2} - 4 \cdot 4 lo g_{10} (5) (- 2 lo g_{10} (5) - 1) = 33 lo g_{10} (5)^{2} + 16 lo g_{10} (5)

x_{1, 2} = \frac{- ( - lo g _{10} ( 5 ) ) \pm 33 lo g _{10} ( 5 ) ^{2} + 16 lo g _{10} ( 5 )}{2 \cdot 4 lo g _{10} ( 5 )}

Separate the solutions

x_{1} = \frac{- ( - lo g _{10} ( 5 ) ) + 33 lo g _{10} ( 5 ) ^{2} + 16 lo g _{10} ( 5 )}{2 \cdot 4 lo g _{10} ( 5 )}, x_{2} = \frac{- ( - lo g _{10} ( 5 ) ) - 33 lo g _{10} ( 5 ) ^{2} + 16 lo g _{10} ( 5 )}{2 \cdot 4 lo g _{10} ( 5 )}

x = \frac{- ( - lo g _{10} ( 5 ) ) + 33 lo g _{10} ( 5 ) ^{2} + 16 lo g _{10} ( 5 )}{2 \cdot 4 lo g _{10} ( 5 )} : \frac{lo g _{10} ( 5 ) + 33 lo g _{10} ( 5 ) ^{2} + 16 lo g _{10} ( 5 )}{8 lo g _{10} ( 5 )}

x = \frac{- ( - lo g _{10} ( 5 ) ) - 33 lo g _{10} ( 5 ) ^{2} + 16 lo g _{10} ( 5 )}{2 \cdot 4 lo g _{10} ( 5 )} : \frac{lo g _{10} ( 5 ) - 33 lo g _{10} ( 5 ) ^{2} + 16 lo g _{10} ( 5 )}{8 lo g _{10} ( 5 )}

The solutions to the quadratic equation are:

x = \frac{lo g _{10} ( 5 ) + 33 lo g _{10} ( 5 ) ^{2} + 16 lo g _{10} ( 5 )}{8 lo g _{10} ( 5 )}, x = \frac{lo g _{10} ( 5 ) - 33 lo g _{10} ( 5 ) ^{2} + 16 lo g _{10} ( 5 )}{8 lo g _{10} ( 5 )}

60 = - 4.9 t^{2} + 20 t + 50

(30 - \frac{2}{3} r)^{2} = 100

s^{2} + 8 s + 16

w^{2} + 6 w - 7 = 0

s^{2} + 8 s + 20

What are the solutions to the equation log_{10}(5)(4x^2+4)-log_{10}(5)(x+6)=1 ?
The solutions to the equation log_{10}(5)(4x^2+4)-log_{10}(5)(x+6)=1 are
Find the zeros of log_{10}(5)(4x^2+4)-log_{10}(5)(x+6)=1
The zeros of log_{10}(5)(4x^2+4)-log_{10}(5)(x+6)=1 are