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

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

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

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

x = - 3

Solution steps

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

Add

lo g_{5} (x + 4)

to both sides

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

y = ln (5 x), x

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

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

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

lo g_{2} (4 x + 9) = 4

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