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

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

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

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

x = 7

Solution steps

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

Add

lo g_{2} (x - 6)

to both sides

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

Simplify

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

Apply log rules

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

Solve

(x - 3) (x - 6) = 4 : 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) = \frac{1}{2}

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

lo g_{5} (b) = 3

lo g_{5} (x) = 0

y ln (y + 2) = 0

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