What are the solutions to the equation (x^2-x-3)log_{10}(4)=3log_{10}(1/4) ?

The solutions to the equation (x^2-x-3)log_{10}(4)=3log_{10}(1/4) are x=0,x=1

Find the zeros of (x^2-x-3)log_{10}(4)=3log_{10}(1/4)

The zeros of (x^2-x-3)log_{10}(4)=3log_{10}(1/4) are x=0,x=1

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(x^{2} - x - 3) lo g_{10} (4) = 3 lo g_{10} (\frac{1}{4})

x = 0, x = 1

Solution steps

(x^{2} - x - 3) lo g_{10} (4) = 3 lo g_{10} (\frac{1}{4})

Move

3 lo g_{10} (\frac{1}{4})

to the left side

(x^{2} - x - 3) lo g_{10} (4) - 3 lo g_{10} (\frac{1}{4}) = 0

Factor

(x^{2} - x - 3) lo g_{10} (4) - 3 lo g_{10} (\frac{1}{4}) : 2 lo g_{10} (2) x (x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0

Solve

x - 1 = 0 : x = 1

The solutions to the quadratic equation are:

x = 0, x = 1

k^{2} - 7 k + 50 = 3

2 y^{2} - 50 = 0

(4 - k) x^{2} - 2 k x = - 9

22 - 6 x^{2} = 0

w^{2} = - 144

What are the solutions to the equation (x^2-x-3)log_{10}(4)=3log_{10}(1/4) ?
The solutions to the equation (x^2-x-3)log_{10}(4)=3log_{10}(1/4) are x=0,x=1
Find the zeros of (x^2-x-3)log_{10}(4)=3log_{10}(1/4)
The zeros of (x^2-x-3)log_{10}(4)=3log_{10}(1/4) are x=0,x=1