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

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

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

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

x = 9

Solution steps

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

Add

lo g_{2} (x - 8)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

x = 9, x = 4

Verify Solutions:

x = 9

True

, x = 4

False

The solution is

x = 9

ln (x^{2}) - 0.7 = 0

0.69 = lo g_{10} (x)

3 ln (2 x) - 4 = 2 ln (2 x)

ln (4 x + 2) = 3

lo g_{2} (2 x - 3) = 4

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