What are the solutions to the equation log_{10}(9)(x^2-4x)=log_{10}(9)(3x-10) ?

The solutions to the equation log_{10}(9)(x^2-4x)=log_{10}(9)(3x-10) are x=2,x=5

Find the zeros of log_{10}(9)(x^2-4x)=log_{10}(9)(3x-10)

The zeros of log_{10}(9)(x^2-4x)=log_{10}(9)(3x-10) are x=2,x=5

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

x = 2, x = 5

Solution steps

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

Move

lo g_{10} (9) (3 x - 10)

to the left side

lo g_{10} (9) (x^{2} - 4 x) - lo g_{10} (9) (3 x - 10) = 0

Factor

lo g_{10} (9) (x^{2} - 4 x) - lo g_{10} (9) (3 x - 10) : 2 lo g_{10} (3) (x - 2) (x - 5)

2 lo g_{10} (3) (x - 2) (x - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x - 5 = 0

Solve

x - 2 = 0 : x = 2

Solve

x - 5 = 0 : x = 5

The solutions to the quadratic equation are:

x = 2, x = 5

3 n^{2} + 4 n + 4 = 0

b (c - a) x^{2} + c (a - b) x + a (b - c) = 0

a, 588 = a^{2} \cdot b

x^{2} - 1000 x - 30000 = 0

x, 12 x^{2} + 5 x y - 2 y^{2} = 0

What are the solutions to the equation log_{10}(9)(x^2-4x)=log_{10}(9)(3x-10) ?
The solutions to the equation log_{10}(9)(x^2-4x)=log_{10}(9)(3x-10) are x=2,x=5
Find the zeros of log_{10}(9)(x^2-4x)=log_{10}(9)(3x-10)
The zeros of log_{10}(9)(x^2-4x)=log_{10}(9)(3x-10) are x=2,x=5