What is the answer to log_{2}(x+5)=3-log_{2}(x-5) ?

The answer to log_{2}(x+5)=3-log_{2}(x-5) is x=sqrt(33)

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log_{2}(x+5)=3-log_{2}(x-5)

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

x = 33

Decimal Notation

x = 5.74456 \dots

Solution steps

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

Add

lo g_{2} (x - 5)

to both sides

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

Simplify

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

Apply log rules

(x + 5) (x - 5) = 8

Solve

(x + 5) (x - 5) = 8 : x = 33, x = - 33

x = 33, x = - 33

Verify Solutions:

x = 33

True

, x = - 33

False

The solution is

x = 33

ln (x^{2} - 4) = 0

ln (x) = 8.699959935

lo g_{3} (5 x - 1) = 4

0.33 = ln (x)

0.33 = ln (y)

What is the answer to log_{2}(x+5)=3-log_{2}(x-5) ?
The answer to log_{2}(x+5)=3-log_{2}(x-5) is x=sqrt(33)
Solve for x: log_{2}(x+5)=3-log_{2}(x-5)
The solution is x=sqrt(33)