What is the answer to log_{2}(x+1)=3-log_{2}(x-1) ?

The answer to log_{2}(x+1)=3-log_{2}(x-1) is x=3

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log_{2}(x+1)=3-log_{2}(x-1)

lo g_{2} (x + 1) = 3 - lo g_{2} (x - 1)

x = 3

Solution steps

lo g_{2} (x + 1) = 3 - lo g_{2} (x - 1)

Add

lo g_{2} (x - 1)

to both sides

lo g_{2} (x + 1) + lo g_{2} (x - 1) = 3 - lo g_{2} (x - 1) + lo g_{2} (x - 1)

Simplify

lo g_{2} (x + 1) + lo g_{2} (x - 1) = 3

Apply log rules

(x + 1) (x - 1) = 8

Solve

(x + 1) (x - 1) = 8 : x = 3, x = - 3

x = 3, x = - 3

Verify Solutions:

x = 3

True

, x = - 3

False

The solution is

x = 3

lo g_{10} (x) = - 16

3 lo g_{10} (x + 1) = 2

s, x = lo g_{10} (s - 4)

0.78 = ln (x)

lo g_{2} (x^{2} - x - 9) = 2

What is the answer to log_{2}(x+1)=3-log_{2}(x-1) ?
The answer to log_{2}(x+1)=3-log_{2}(x-1) is x=3
Solve for x: log_{2}(x+1)=3-log_{2}(x-1)
The solution is x=3