What is the answer to log_{2}(x+7)-log_{2}(x-1)=1 ?

The answer to log_{2}(x+7)-log_{2}(x-1)=1 is x=9

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log_{2}(x+7)-log_{2}(x-1)=1

lo g_{2} (x + 7) - lo g_{2} (x - 1) = 1

x = 9

Solution steps

lo g_{2} (x + 7) - lo g_{2} (x - 1) = 1

Add

lo g_{2} (x - 1)

to both sides

lo g_{2} (x + 7) - lo g_{2} (x - 1) + lo g_{2} (x - 1) = 1 + lo g_{2} (x - 1)

Simplify

lo g_{2} (x + 7) = 1 + lo g_{2} (x - 1)

Apply log rules

x + 7 = 2 (x - 1)

Solve

x + 7 = 2 (x - 1) : x = 9

x = 9

Verify Solutions:

x = 9

True

The solution is

x = 9

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

lo g_{b} (4) = \frac{2}{3}

ln (x) + ln (x - 2) = ln (35)

ln (a) = 2

lo g_{5} (lo g_{3} (x)) = 0

What is the answer to log_{2}(x+7)-log_{2}(x-1)=1 ?
The answer to log_{2}(x+7)-log_{2}(x-1)=1 is x=9
Solve for x: log_{2}(x+7)-log_{2}(x-1)=1
The solution is x=9