What is the answer to log_{5}(x+8)=1-log_{5}(x+4) ?

The answer to log_{5}(x+8)=1-log_{5}(x+4) is x=-3

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log_{5}(x+8)=1-log_{5}(x+4)

lo g_{5} (x + 8) = 1 - lo g_{5} (x + 4)

x = - 3

Solution steps

lo g_{5} (x + 8) = 1 - lo g_{5} (x + 4)

Add

lo g_{5} (x + 4)

to both sides

lo g_{5} (x + 8) + lo g_{5} (x + 4) = 1 - lo g_{5} (x + 4) + lo g_{5} (x + 4)

Simplify

lo g_{5} (x + 8) + lo g_{5} (x + 4) = 1

Apply log rules

(x + 8) (x + 4) = 5

Solve

(x + 8) (x + 4) = 5 : x = - 3, x = - 9

x = - 3, x = - 9

Verify Solutions:

x = - 3

True

, x = - 9

False

The solution is

x = - 3

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

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

lo g_{3} (x - 6) + lo g_{3} (x) = 3

4.76 = - lo g_{10} (x)

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

What is the answer to log_{5}(x+8)=1-log_{5}(x+4) ?
The answer to log_{5}(x+8)=1-log_{5}(x+4) is x=-3
Solve for x: log_{5}(x+8)=1-log_{5}(x+4)
The solution is x=-3