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

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

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

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

x = 7

Solution steps

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

Add

lo g_{2} (x - 3)

to both sides

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

Simplify

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

Apply log rules

(x - 6) (x - 3) = 4

Solve

(x - 6) (x - 3) = 4 : x = 7, x = 2

x = 7, x = 2

Verify Solutions:

x = 7

True

, x = 2

False

The solution is

x = 7

lo g_{10} (x) = 10

lo g_{a} (x^{2}) - 4 = 2 lo g_{a} (6)

lo g_{x} (9) = - 2

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

ln (x^{2}) = 10

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