What is the answer to log_{2}(x^2-4)-log_{2}(x-2)=3 ?

The answer to log_{2}(x^2-4)-log_{2}(x-2)=3 is x=6

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log_{2}(x^2-4)-log_{2}(x-2)=3

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

x = 6

Solution steps

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

Add

lo g_{2} (x - 2)

to both sides

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

Simplify

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

Apply log rules

x^{2} - 4 = 8 (x - 2)

Solve

x^{2} - 4 = 8 (x - 2) : x = 6, x = 2

x = 6, x = 2

Verify Solutions:

x = 6

True

, x = 2

False

The solution is

x = 6

lo g_{3} (4 x^{3} + 14 x^{2} + 13 x + 3) = lo g_{3} (x + 1)

lo g_{10} (8 x) = \frac{7}{3}

ln (x + 5) - ln (x) = 3

lo g_{10} (n) = - 0.1302

ln (4 x - 2) = 5

What is the answer to log_{2}(x^2-4)-log_{2}(x-2)=3 ?
The answer to log_{2}(x^2-4)-log_{2}(x-2)=3 is x=6
Solve for x: log_{2}(x^2-4)-log_{2}(x-2)=3
The solution is x=6