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

The answer to log_{2}(x-5)=2-log_{2}(x-2) is x=6

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

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

x = 6

Solution steps

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

Add

lo g_{2} (x - 2)

to both sides

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

Simplify

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

Apply log rules

(x - 5) (x - 2) = 4

Solve

(x - 5) (x - 2) = 4 : x = 6, x = 1

x = 6, x = 1

Verify Solutions:

x = 6

True

, x = 1

False

The solution is

x = 6

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

lo g_{10} (x) + lo g_{10} (4) = 0

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

x, ln (y) = ln (1 + x) + c

lo g_{2} (x^{2}) = 6

What is the answer to log_{2}(x-5)=2-log_{2}(x-2) ?
The answer to log_{2}(x-5)=2-log_{2}(x-2) is x=6
Solve for x: log_{2}(x-5)=2-log_{2}(x-2)
The solution is x=6