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

The answer to log_{2}(x+5)=3-log_{2}(x+3) is x=-1

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

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

x = - 1

Solution steps

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

Add

lo g_{2} (x + 3)

to both sides

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

Simplify

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

Apply log rules

(x + 5) (x + 3) = 8

Solve

(x + 5) (x + 3) = 8 : x = - 1, x = - 7

x = - 1, x = - 7

Verify Solutions:

x = - 1

True

, x = - 7

False

The solution is

x = - 1

lo g_{5} (x) + lo g_{5} (30) = 3

ln (x) + ln (x + 3) = 4

ln (x) + ln (x + 3) = 2 ln (x + 1)

- 5 + lo g_{2} (x + 8) = - 1

lo g_{x} (2) = \frac{1}{4}

What is the answer to log_{2}(x+5)=3-log_{2}(x+3) ?
The answer to log_{2}(x+5)=3-log_{2}(x+3) is x=-1
Solve for x: log_{2}(x+5)=3-log_{2}(x+3)
The solution is x=-1