What is the answer to log_{2}(x^2-25)-log_{2}(x-5)=4 ?

The answer to log_{2}(x^2-25)-log_{2}(x-5)=4 is x=11

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log_{2}(x^2-25)-log_{2}(x-5)=4

lo g_{2} (x^{2} - 25) - lo g_{2} (x - 5) = 4

x = 11

Solution steps

lo g_{2} (x^{2} - 25) - lo g_{2} (x - 5) = 4

Add

lo g_{2} (x - 5)

to both sides

lo g_{2} (x^{2} - 25) - lo g_{2} (x - 5) + lo g_{2} (x - 5) = 4 + lo g_{2} (x - 5)

Simplify

lo g_{2} (x^{2} - 25) = 4 + lo g_{2} (x - 5)

Apply log rules

x^{2} - 25 = 16 (x - 5)

Solve

x^{2} - 25 = 16 (x - 5) : x = 11, x = 5

x = 11, x = 5

Verify Solutions:

x = 11

True

, x = 5

False

The solution is

x = 11

lo g_{4} (5 p - 6) = lo g_{4} (4 p + 2)

lo g_{2} (3 x^{2} + 7 x) = 3

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

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

2 lo g_{10} (x) - lo g_{10} (2 x + 15) = 0

What is the answer to log_{2}(x^2-25)-log_{2}(x-5)=4 ?
The answer to log_{2}(x^2-25)-log_{2}(x-5)=4 is x=11
Solve for x: log_{2}(x^2-25)-log_{2}(x-5)=4
The solution is x=11