What are the solutions to the equation log_{10}(2)(x^2-3x)=2 ?

The solutions to the equation log_{10}(2)(x^2-3x)=2 are

Find the zeros of log_{10}(2)(x^2-3x)=2

The zeros of log_{10}(2)(x^2-3x)=2 are

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lo g_{10} (2) (x^{2} - 3 x) = 2

x = \frac{3 lo g _{10} ( 2 ) + 9 lo g _{10} ( 2 ) ^{2} + 8 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}, x = \frac{3 lo g _{10} ( 2 ) - 9 lo g _{10} ( 2 ) ^{2} + 8 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

Decimal Notation

x = 4.48225 \dots, x = - 1.48225 \dots

Solution steps

lo g_{10} (2) (x^{2} - 3 x) = 2

Expand

lo g_{10} (2) (x^{2} - 3 x) : lo g_{10} (2) x^{2} - 3 lo g_{10} (2) x

lo g_{10} (2) x^{2} - 3 lo g_{10} (2) x = 2

Move

2

to the left side

lo g_{10} (2) x^{2} - 3 lo g_{10} (2) x - 2 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 lo g _{10} ( 2 ) ) \pm ( - 3 lo g _{10} ( 2 ) ) ^{2} - 4 lo g _{10} ( 2 ) ( - 2 )}{2 lo g _{10} ( 2 )}

(- 3 lo g_{10} (2))^{2} - 4 lo g_{10} (2) (- 2) = 9 lo g_{10} (2)^{2} + 8 lo g_{10} (2)

x_{1, 2} = \frac{- ( - 3 lo g _{10} ( 2 ) ) \pm 9 lo g _{10} ( 2 ) ^{2} + 8 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

Separate the solutions

x_{1} = \frac{- ( - 3 lo g _{10} ( 2 ) ) + 9 lo g _{10} ( 2 ) ^{2} + 8 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}, x_{2} = \frac{- ( - 3 lo g _{10} ( 2 ) ) - 9 lo g _{10} ( 2 ) ^{2} + 8 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

x = \frac{- ( - 3 lo g _{10} ( 2 ) ) + 9 lo g _{10} ( 2 ) ^{2} + 8 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )} : \frac{3 lo g _{10} ( 2 ) + 9 lo g _{10} ( 2 ) ^{2} + 8 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

x = \frac{- ( - 3 lo g _{10} ( 2 ) ) - 9 lo g _{10} ( 2 ) ^{2} + 8 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )} : \frac{3 lo g _{10} ( 2 ) - 9 lo g _{10} ( 2 ) ^{2} + 8 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

The solutions to the quadratic equation are:

x = \frac{3 lo g _{10} ( 2 ) + 9 lo g _{10} ( 2 ) ^{2} + 8 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}, x = \frac{3 lo g _{10} ( 2 ) - 9 lo g _{10} ( 2 ) ^{2} + 8 lo g _{10} ( 2 )}{2 lo g _{10} ( 2 )}

p^{2} + 2 p - 13 = - 5 - 5

(2 R - 1) (R - 2) = 0

8 x^{2} + 36 x = 0

5 a^{2} - 8 a - 4 = 0

x^{2} + 2 x - 8 = 1

What are the solutions to the equation log_{10}(2)(x^2-3x)=2 ?
The solutions to the equation log_{10}(2)(x^2-3x)=2 are
Find the zeros of log_{10}(2)(x^2-3x)=2
The zeros of log_{10}(2)(x^2-3x)=2 are