What is the answer to log_{2}(x-8)=2-log_{2}(x-5) ?

The answer to log_{2}(x-8)=2-log_{2}(x-5) is x=9

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log_{2}(x-8)=2-log_{2}(x-5)

lo g_{2} (x - 8) = 2 - lo g_{2} (x - 5)

x = 9

Solution steps

lo g_{2} (x - 8) = 2 - lo g_{2} (x - 5)

Add

lo g_{2} (x - 5)

to both sides

lo g_{2} (x - 8) + lo g_{2} (x - 5) = 2 - lo g_{2} (x - 5) + lo g_{2} (x - 5)

Simplify

lo g_{2} (x - 8) + lo g_{2} (x - 5) = 2

Apply log rules

(x - 8) (x - 5) = 4

Solve

(x - 8) (x - 5) = 4 : x = 9, x = 4

x = 9, x = 4

Verify Solutions:

x = 9

True

, x = 4

False

The solution is

x = 9

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

lo g_{x} (25) = \frac{2}{3}

lo g_{4} (15 x + 1) = 2

lo g_{x} (64) = lo g_{5} (125)

lo g_{10} (x) + lo g_{10} (3) = 2

What is the answer to log_{2}(x-8)=2-log_{2}(x-5) ?
The answer to log_{2}(x-8)=2-log_{2}(x-5) is x=9
Solve for x: log_{2}(x-8)=2-log_{2}(x-5)
The solution is x=9