What is the answer to log_{2}(x+2)-log_{2}(x-4)=2 ?

The answer to log_{2}(x+2)-log_{2}(x-4)=2 is x=6

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log_{2}(x+2)-log_{2}(x-4)=2

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

x = 6

Solution steps

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

Add

lo g_{2} (x - 4)

to both sides

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

Simplify

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

Apply log rules

x + 2 = 4 (x - 4)

Solve

x + 2 = 4 (x - 4) : x = 6

x = 6

Verify Solutions:

x = 6

True

The solution is

x = 6

5 = 1 + 3.3 lo g_{10} (n)

lo g_{0.5} (2 x + 59) = - 2

x = ln (- 3 x)

ln (x) + ln (2 x) = 8

ln (x) + ln (2 x) = 7

What is the answer to log_{2}(x+2)-log_{2}(x-4)=2 ?
The answer to log_{2}(x+2)-log_{2}(x-4)=2 is x=6
Solve for x: log_{2}(x+2)-log_{2}(x-4)=2
The solution is x=6