What is the answer to log_{2}(x-6)+log_{2}(x+1)=3 ?

The answer to log_{2}(x-6)+log_{2}(x+1)=3 is x=7

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log_{2}(x-6)+log_{2}(x+1)=3

lo g_{2} (x - 6) + lo g_{2} (x + 1) = 3

x = 7

Solution steps

lo g_{2} (x - 6) + lo g_{2} (x + 1) = 3

Apply log rules

(x - 6) (x + 1) = 8

Solve

(x - 6) (x + 1) = 8 : x = 7, x = - 2

x = 7, x = - 2

Verify Solutions:

x = 7

True

, x = - 2

False

The solution is

x = 7

lo g_{5} (x - 8) = 1 - lo g_{5} (x - 4)

lo g_{8} (x) = - 2

lo g_{2} (x) - lo g_{x} (4) = 1

lo g_{5} (x - 2) = lo g_{5} (3 x + 7)

lo g_{10} (x) + lo g_{10} (3) = 1

What is the answer to log_{2}(x-6)+log_{2}(x+1)=3 ?
The answer to log_{2}(x-6)+log_{2}(x+1)=3 is x=7
Solve for x: log_{2}(x-6)+log_{2}(x+1)=3
The solution is x=7