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

The answer to log_{2}(x-3)=2-log_{2}(x) is x=4

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

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

x = 4

Solution steps

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

Add

lo g_{2} (x)

to both sides

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

Simplify

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

Apply log rules

(x - 3) x = 4

Solve

(x - 3) x = 4 : x = 4, x = - 1

x = 4, x = - 1

Verify Solutions:

x = 4

True

, x = - 1

False

The solution is

x = 4

7 = lo g_{10} (x)

lo g_{7} (3 x) = 3

lo g_{10} (3 x - 5) = 3

10.4 = - lo g_{10} (x)

lo g_{10} (y) = 2 - lo g_{10} (y - 21)

What is the answer to log_{2}(x-3)=2-log_{2}(x) ?
The answer to log_{2}(x-3)=2-log_{2}(x) is x=4
Solve for x: log_{2}(x-3)=2-log_{2}(x)
The solution is x=4