What is the answer to log_{2}(x-1)+log_{2}(x+3)=5 ?

The answer to log_{2}(x-1)+log_{2}(x+3)=5 is x=5

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log_{2}(x-1)+log_{2}(x+3)=5

lo g_{2} (x - 1) + lo g_{2} (x + 3) = 5

x = 5

Solution steps

lo g_{2} (x - 1) + lo g_{2} (x + 3) = 5

Apply log rules

(x - 1) (x + 3) = 32

Solve

(x - 1) (x + 3) = 32 : x = 5, x = - 7

x = 5, x = - 7

Verify Solutions:

x = 5

True

, x = - 7

False

The solution is

x = 5

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

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

(lo g_{2} (x))^{2} + 2 \cdot lo g_{2} (x) - 2 = 0

(lo g_{10} (10 x)) 2 - 4 lo g_{10} (10 x) - 5 = 0

6 lo g_{10} (a) + 6 lo g_{10} (a - 9) = 2

What is the answer to log_{2}(x-1)+log_{2}(x+3)=5 ?
The answer to log_{2}(x-1)+log_{2}(x+3)=5 is x=5
Solve for x: log_{2}(x-1)+log_{2}(x+3)=5
The solution is x=5